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class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.03795">arXiv:2408.03795</a> <span> [<a href="https://arxiv.org/pdf/2408.03795">pdf</a>, <a href="https://arxiv.org/format/2408.03795">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Frank's triangular norms in Piaget's logical proportions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Richard%2C+G">Gilles Richard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.03795v1-abstract-short" style="display: inline;"> Starting from the Boolean notion of logical proportion in Piaget's sense, which turns out to be equivalent to analogical proportion, this note proposes a definition of analogical proportion between numerical values based on triangular norms (and dual co-norms). Frank's family of triangular norms is particularly interesting from this perspective. The article concludes with a comparative discussion… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03795v1-abstract-full').style.display = 'inline'; document.getElementById('2408.03795v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.03795v1-abstract-full" style="display: none;"> Starting from the Boolean notion of logical proportion in Piaget's sense, which turns out to be equivalent to analogical proportion, this note proposes a definition of analogical proportion between numerical values based on triangular norms (and dual co-norms). Frank's family of triangular norms is particularly interesting from this perspective. The article concludes with a comparative discussion with another very recent proposal for defining analogical proportions between numerical values based on the family of generalized means. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.03795v1-abstract-full').style.display = 'none'; document.getElementById('2408.03795v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 August, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2310.13500">arXiv:2310.13500</a> <span> [<a href="https://arxiv.org/pdf/2310.13500">pdf</a>, <a href="https://arxiv.org/format/2310.13500">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Analogical Proportions and Creativity: A Preliminary Study </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Afantenos%2C+S">Stergos Afantenos</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Bernardes%2C+L+C">Leonardo Cortez Bernardes</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2310.13500v1-abstract-short" style="display: inline;"> Analogical proportions are statements of the form "$a$ is to $b$ as $c$ is to $d$", which expresses that the comparisons of the elements in pair $(a, b)$ and in pair $(c, d)$ yield similar results. Analogical proportions are creative in the sense that given 3 distinct items, the representation of a 4th item $d$, distinct from the previous items, which forms an analogical proportion with them can b… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.13500v1-abstract-full').style.display = 'inline'; document.getElementById('2310.13500v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2310.13500v1-abstract-full" style="display: none;"> Analogical proportions are statements of the form "$a$ is to $b$ as $c$ is to $d$", which expresses that the comparisons of the elements in pair $(a, b)$ and in pair $(c, d)$ yield similar results. Analogical proportions are creative in the sense that given 3 distinct items, the representation of a 4th item $d$, distinct from the previous items, which forms an analogical proportion with them can be calculated, provided certain conditions are met. After providing an introduction to analogical proportions and their properties, the paper reports the results of an experiment made with a database of animal descriptions and their class, where we try to "create" new animals from existing ones, retrieving rare animals such as platypus. We perform a series of experiments using word embeddings as well as Boolean features in order to propose novel animals based on analogical proportions, showing that word embeddings obtain better results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.13500v1-abstract-full').style.display = 'none'; document.getElementById('2310.13500v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.02009">arXiv:2309.02009</a> <span> [<a href="https://arxiv.org/pdf/2309.02009">pdf</a>, <a href="https://arxiv.org/ps/2309.02009">ps</a>, <a href="https://arxiv.org/format/2309.02009">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1080/11663081.2023.2244379">10.1080/11663081.2023.2244379 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Belief revision and incongruity: is it a joke? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Bannay%2C+F+D+d+S+C+-">Florence Dupin de Saint Cyr - Bannay</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2309.02009v1-abstract-short" style="display: inline;"> Incongruity often makes people laugh. You have to be smart to say stupid things. It requires to be even smarter for understanding them. This paper is a shameless attempt to formalize this intelligent behavior in the case of an agent listening to a joke. All this is a matter of revision of beliefs, surprise and violation of norms. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.02009v1-abstract-full" style="display: none;"> Incongruity often makes people laugh. You have to be smart to say stupid things. It requires to be even smarter for understanding them. This paper is a shameless attempt to formalize this intelligent behavior in the case of an agent listening to a joke. All this is a matter of revision of beliefs, surprise and violation of norms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.02009v1-abstract-full').style.display = 'none'; document.getElementById('2309.02009v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">A special paper on/in humor/honor for/of Philippe Besnard</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Journal of Applied Non-Classical Logics, In press, Special issue in honour of Philippe Besnard, pp.1-28 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.13168">arXiv:2303.13168</a> <span> [<a href="https://arxiv.org/pdf/2303.13168">pdf</a>, <a href="https://arxiv.org/ps/2303.13168">ps</a>, <a href="https://arxiv.org/format/2303.13168">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Logic in Computer Science">cs.LO</span> </div> </div> <p class="title is-5 mathjax"> An elementary belief function logic </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Godo%2C+L">Lluis Godo</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.13168v1-abstract-short" style="display: inline;"> Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and plausibility functions as well as between upper and lower probabilities extend the duality between possibility and necessity modalities to the graded environment. It has b… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.13168v1-abstract-full').style.display = 'inline'; document.getElementById('2303.13168v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.13168v1-abstract-full" style="display: none;"> Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and plausibility functions as well as between upper and lower probabilities extend the duality between possibility and necessity modalities to the graded environment. It has been shown that the all-or-nothing version of possibility theory can be exactly captured by a minimal epistemic logic (MEL) that uses a very small fragment of the KD modal logic, without resorting to relational semantics. Besides, the case of belief functions has been studied independently, and a belief function logic has been obtained by extending the modal logic S5 to graded modalities using 艁ukasiewicz logic, albeit using relational semantics. This paper shows that a simpler belief function logic can be devised by adding 艁ukasiewicz logic on top of MEL. It allows for a more natural semantics in terms of Shafer basic probability assignments. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.13168v1-abstract-full').style.display = 'none'; document.getElementById('2303.13168v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2301.04134">arXiv:2301.04134</a> <span> [<a href="https://arxiv.org/pdf/2301.04134">pdf</a>, <a href="https://arxiv.org/format/2301.04134">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Analogical Relevance Index </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Lim%2C+S">Suryani Lim</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Richard%2C+G">Gilles Richard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2301.04134v1-abstract-short" style="display: inline;"> Focusing on the most significant features of a dataset is useful both in machine learning (ML) and data mining. In ML, it can lead to a higher accuracy, a faster learning process, and ultimately a simpler and more understandable model. In data mining, identifying significant features is essential not only for gaining a better understanding of the data but also for visualization. In this paper, we… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.04134v1-abstract-full').style.display = 'inline'; document.getElementById('2301.04134v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2301.04134v1-abstract-full" style="display: none;"> Focusing on the most significant features of a dataset is useful both in machine learning (ML) and data mining. In ML, it can lead to a higher accuracy, a faster learning process, and ultimately a simpler and more understandable model. In data mining, identifying significant features is essential not only for gaining a better understanding of the data but also for visualization. In this paper, we demonstrate a new way of identifying significant features inspired by analogical proportions. Such a proportion is of the form of "a is to b as c is to d", comparing two pairs of items (a, b) and (c, d) in terms of similarities and dissimilarities. In a classification context, if the similarities/dissimilarities between a and b correlate with the fact that a and b have different labels, this knowledge can be transferred to c and d, inferring that c and d also have different labels. From a feature selection perspective, observing a huge number of such pairs (a, b) where a and b have different labels provides a hint about the importance of the features where a and b differ. Following this idea, we introduce the Analogical Relevance Index (ARI), a new statistical test of the significance of a given feature with respect to the label. ARI is a filter-based method. Filter-based methods are ML-agnostic but generally unable to handle feature redundancy. However, ARI can detect feature redundancy. Our experiments show that ARI is effective and outperforms well-known methods on a variety of artificial and some real datasets. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2301.04134v1-abstract-full').style.display = 'none'; document.getElementById('2301.04134v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages, 5 figures, 6 tables</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.11717">arXiv:2212.11717</a> <span> [<a href="https://arxiv.org/pdf/2212.11717">pdf</a>, <a href="https://arxiv.org/ps/2212.11717">ps</a>, <a href="https://arxiv.org/format/2212.11717">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Some recent advances in reasoning based on analogical proportions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Bounhas%2C+M">Myriam Bounhas</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Richard%2C+G">Gilles Richard</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.11717v1-abstract-short" style="display: inline;"> Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference in terms of accuracy and in terms of computational cost. Then it indicates the potential of analogical proportions for explanation. Finally, it highlights the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11717v1-abstract-full').style.display = 'inline'; document.getElementById('2212.11717v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.11717v1-abstract-full" style="display: none;"> Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference in terms of accuracy and in terms of computational cost. Then it indicates the potential of analogical proportions for explanation. Finally, it highlights the close relationship between analogical proportions and multi-valued dependencies, which reveals an unsuspected aspect of the former. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11717v1-abstract-full').style.display = 'none'; document.getElementById('2212.11717v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.06612">arXiv:1912.06612</a> <span> [<a href="https://arxiv.org/pdf/1912.06612">pdf</a>, <a href="https://arxiv.org/ps/1912.06612">ps</a>, <a href="https://arxiv.org/format/1912.06612">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> From Shallow to Deep Interactions Between Knowledge Representation, Reasoning and Machine Learning (Kay R. Amel group) </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Bouraoui%2C+Z">Zied Bouraoui</a>, <a href="/search/?searchtype=author&query=Cornu%C3%A9jols%2C+A">Antoine Cornu茅jols</a>, <a href="/search/?searchtype=author&query=Den%C5%93ux%2C+T">Thierry Den艙ux</a>, <a href="/search/?searchtype=author&query=Destercke%2C+S">S茅bastien Destercke</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Guillaume%2C+R">Romain Guillaume</a>, <a href="/search/?searchtype=author&query=Marques-Silva%2C+J">Jo茫o Marques-Silva</a>, <a href="/search/?searchtype=author&query=Mengin%2C+J">J茅r么me Mengin</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Schockaert%2C+S">Steven Schockaert</a>, <a href="/search/?searchtype=author&query=Serrurier%2C+M">Mathieu Serrurier</a>, <a href="/search/?searchtype=author&query=Vrain%2C+C">Christel Vrain</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1912.06612v1-abstract-short" style="display: inline;"> This paper proposes a tentative and original survey of meeting points between Knowledge Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have been developing quite separately in the last three decades. Some common concerns are identified and discussed such as the types of used representation, the roles of knowledge and data, the lack or the excess of information, or th… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.06612v1-abstract-full').style.display = 'inline'; document.getElementById('1912.06612v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.06612v1-abstract-full" style="display: none;"> This paper proposes a tentative and original survey of meeting points between Knowledge Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have been developing quite separately in the last three decades. Some common concerns are identified and discussed such as the types of used representation, the roles of knowledge and data, the lack or the excess of information, or the need for explanations and causal understanding. Then some methodologies combining reasoning and learning are reviewed (such as inductive logic programming, neuro-symbolic reasoning, formal concept analysis, rule-based representations and ML, uncertainty in ML, or case-based reasoning and analogical reasoning), before discussing examples of synergies between KRR and ML (including topics such as belief functions on regression, EM algorithm versus revision, the semantic description of vector representations, the combination of deep learning with high level inference, knowledge graph completion, declarative frameworks for data mining, or preferences and recommendation). This paper is the first step of a work in progress aiming at a better mutual understanding of research in KRR and ML, and how they could cooperate. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.06612v1-abstract-full').style.display = 'none'; document.getElementById('1912.06612v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">53 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1304.3843">arXiv:1304.3843</a> <span>  </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (1999) </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Laskey%2C+K">Kathryn Laskey</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1304.3843v2-abstract-short" style="display: inline;"> This is the Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, which was held in Stockholm Sweden, July 30 - August 1, 1999 </span> <span class="abstract-full has-text-grey-dark mathjax" id="1304.3843v2-abstract-full" style="display: none;"> This is the Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, which was held in Stockholm Sweden, July 30 - August 1, 1999 <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.3843v2-abstract-full').style.display = 'none'; document.getElementById('1304.3843v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 August, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 April, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI1999 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1304.2349">arXiv:1304.2349</a> <span> [<a href="https://arxiv.org/pdf/1304.2349">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Modeling uncertain and vague knowledge in possibility and evidence theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1304.2349v1-abstract-short" style="display: inline;"> This paper advocates the usefulness of new theories of uncertainty for the purpose of modeling some facets of uncertain knowledge, especially vagueness, in AI. It can be viewed as a partial reply to Cheeseman's (among others) defense of probability. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1304.2349v1-abstract-full" style="display: none;"> This paper advocates the usefulness of new theories of uncertainty for the purpose of modeling some facets of uncertain knowledge, especially vagueness, in AI. It can be viewed as a partial reply to Cheeseman's (among others) defense of probability. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.2349v1-abstract-full').style.display = 'none'; document.getElementById('1304.2349v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Fourth Conference on Uncertainty in Artificial Intelligence (UAI1988)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1988-PG-81-89 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1304.1502">arXiv:1304.1502</a> <span> [<a href="https://arxiv.org/pdf/1304.1502">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Positive and Negative Explanations of Uncertain Reasoning in the Framework of Possibility Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Farrency%2C+H">Henri Farrency</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1304.1502v1-abstract-short" style="display: inline;"> This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the available information concerning the value of a logical or numerical variable is represented by a possibility distribution which restricts its more or less possi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1502v1-abstract-full').style.display = 'inline'; document.getElementById('1304.1502v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1304.1502v1-abstract-full" style="display: none;"> This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the available information concerning the value of a logical or numerical variable is represented by a possibility distribution which restricts its more or less possible values. We first discuss different kinds of queries asking for explanations before focusing on the two following types : i) how, a particular possibility distribution is obtained (emphasizing the main reasons only) ; ii) why in a computed possibility distribution, a particular value has received a possibility degree which is so high, so low or so contrary to the expectation. The approach is based on the exploitation of equations in max-min algebra. This formalism includes the limit case of certain and precise information. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1502v1-abstract-full').style.display = 'none'; document.getElementById('1304.1502v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Fifth Conference on Uncertainty in Artificial Intelligence (UAI1989)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1989-PG-95-101 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1304.1500">arXiv:1304.1500</a> <span> [<a href="https://arxiv.org/pdf/1304.1500">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Automated Reasoning Using Possibilistic Logic: Semantics, Belief Revision and Variable Certainty Weights </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Lang%2C+J">Jerome Lang</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1304.1500v1-abstract-short" style="display: inline;"> In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure, according to the nature of the uncertainty. Two resolution rules are used for coping with the different situations, and the refutation method can be generalized. Besi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1500v1-abstract-full').style.display = 'inline'; document.getElementById('1304.1500v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1304.1500v1-abstract-full" style="display: none;"> In this paper an approach to automated deduction under uncertainty,based on possibilistic logic, is proposed ; for that purpose we deal with clauses weighted by a degree which is a lower bound of a necessity or a possibility measure, according to the nature of the uncertainty. Two resolution rules are used for coping with the different situations, and the refutation method can be generalized. Besides the lower bounds are allowed to be functions of variables involved in the clause, which gives hypothetical reasoning capabilities. The relation between our approach and the idea of minimizing abnormality is briefly discussed. In case where only lower bounds of necessity measures are involved, a semantics is proposed, in which the completeness of the extended resolution principle is proved. Moreover deduction from a partially inconsistent knowledge base can be managed in this approach and displays some form of non-monotonicity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1500v1-abstract-full').style.display = 'none'; document.getElementById('1304.1500v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Fifth Conference on Uncertainty in Artificial Intelligence (UAI1989)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1989-PG-81-87 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1304.1118">arXiv:1304.1118</a> <span> [<a href="https://arxiv.org/pdf/1304.1118">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Updating with Belief Functions, Ordinal Conditioning Functions and Possibility Measures </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1304.1118v1-abstract-short" style="display: inline;"> This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely: Shafer's evidence theory, Zadeh's possibility theory, Spohn's theory of epistemic states. In the two first cases, analogues of Jeffrey's rule of conditioning a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1118v1-abstract-full').style.display = 'inline'; document.getElementById('1304.1118v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1304.1118v1-abstract-full" style="display: none;"> This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely: Shafer's evidence theory, Zadeh's possibility theory, Spohn's theory of epistemic states. In the two first cases, analogues of Jeffrey's rule of conditioning are introduced and discussed. The relations between Spohn's model and possibility theory are emphasized and Spohn's updating rule is contrasted with the Jeffrey-like rule of conditioning in possibility theory. Recent results by Shenoy on the combination of ordinal conditional functions are reinterpreted in the language of possibility theory. It is shown that Shenoy's combination rule has a well-known possibilistic counterpart. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1304.1118v1-abstract-full').style.display = 'none'; document.getElementById('1304.1118v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence (UAI1990)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1990-PG-307-316 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.5727">arXiv:1303.5727</a> <span> [<a href="https://arxiv.org/pdf/1303.5727">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Logic in Computer Science">cs.LO</span> </div> </div> <p class="title is-5 mathjax"> A Logic of Graded Possibility and Certainty Coping with Partial Inconsistency </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Lang%2C+J">Jerome Lang</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.5727v1-abstract-short" style="display: inline;"> A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzz… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.5727v1-abstract-full').style.display = 'inline'; document.getElementById('1303.5727v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.5727v1-abstract-full" style="display: none;"> A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzzy sets of interpretations, each fuzzy set representing a possibility distribution describing what is known about the state of the world. A possibilistic knowledge base is then viewed as a set of possibility distributions that satisfy it. The refutation method of automated deduction in possibilistic logic, based on previously introduced generalized resolution principle is proved to be sound and complete with respect to the proposed semantics, including the case of partial inconsistency. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.5727v1-abstract-full').style.display = 'none'; document.getElementById('1303.5727v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1991-PG-188-196 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.5706">arXiv:1303.5706</a> <span> [<a href="https://arxiv.org/pdf/1303.5706">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Constraint Propagation with Imprecise Conditional Probabilities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Amarger%2C+S">Stephane Amarger</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.5706v1-abstract-short" style="display: inline;"> An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation rules which provide the best bracketing of a conditional probability of interest from the knowledge of the bracketing of some other conditional probabilities. A p… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.5706v1-abstract-full').style.display = 'inline'; document.getElementById('1303.5706v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.5706v1-abstract-full" style="display: none;"> An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation rules which provide the best bracketing of a conditional probability of interest from the knowledge of the bracketing of some other conditional probabilities. A procedure that uses two such propagation rules repeatedly is proposed in order to estimate any simple conditional probability of interest from the available knowledge. The iterative procedure, that does not require independence assumptions, looks promising with respect to the linear programming method. Improved bounds for conditional probabilities are given when independence assumptions hold. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.5706v1-abstract-full').style.display = 'none'; document.getElementById('1303.5706v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1991-PG-26-34 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.5401">arXiv:1303.5401</a> <span> [<a href="https://arxiv.org/pdf/1303.5401">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> A Symbolic Approach to Reasoning with Linguistic Quantifiers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Godo%2C+L">Lluis Godo</a>, <a href="/search/?searchtype=author&query=de+Mantaras%2C+R+L">Ramon Lopez de Mantaras</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.5401v1-abstract-short" style="display: inline;"> This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions. Then instead of propagating numbers, qualitative terms are propagated in accordance with the numerical interpretation of these terms. The quantified syllogi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.5401v1-abstract-full').style.display = 'inline'; document.getElementById('1303.5401v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.5401v1-abstract-full" style="display: none;"> This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions. Then instead of propagating numbers, qualitative terms are propagated in accordance with the numerical interpretation of these terms. The quantified syllogism, modelling the chaining of probabilistic rules, is studied in this context. It is shown that a qualitative counterpart of this syllogism makes sense, and is relatively independent of the threshold defining the linguistically meaningful intervals, provided that these threshold values remain in accordance with the intuition. The inference power is less than that of a full-fledged probabilistic con-quaint propagation device but better corresponds to what could be thought of as commonsense probabilistic reasoning. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.5401v1-abstract-full').style.display = 'none'; document.getElementById('1303.5401v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence (UAI1992)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1992-PG-74-82 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.1503">arXiv:1303.1503</a> <span> [<a href="https://arxiv.org/pdf/1303.1503">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Argumentative inference in uncertain and inconsistent knowledge bases </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Benferhat%2C+S">Salem Benferhat</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.1503v1-abstract-short" style="display: inline;"> This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the absence of consistent arguments in favor of its contrary, is particularly investigated. Flat knowledge bases, i.e. without any priority between their elements, a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.1503v1-abstract-full').style.display = 'inline'; document.getElementById('1303.1503v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.1503v1-abstract-full" style="display: none;"> This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the absence of consistent arguments in favor of its contrary, is particularly investigated. Flat knowledge bases, i.e. without any priority between their elements, as well as prioritized ones where some elements are considered as more strongly entrenched than others are studied under different consequence relations. Lastly a paraconsistent-like treatment of prioritized knowledge bases is proposed, where both the level of entrenchment and the level of paraconsistency attached to a formula are propagated. The priority levels are handled in the framework of possibility theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.1503v1-abstract-full').style.display = 'none'; document.getElementById('1303.1503v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1993-PG-411-419 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1303.1466">arXiv:1303.1466</a> <span> [<a href="https://arxiv.org/pdf/1303.1466">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> A fuzzy relation-based extension of Reggia's relational model for diagnosis handling uncertain and incomplete information </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1303.1466v1-abstract-short" style="display: inline;"> Relational models for diagnosis are based on a direct description of the association between disorders and manifestations. This type of model has been specially used and developed by Reggia and his co-workers in the late eighties as a basic starting point for approaching diagnosis problems. The paper proposes a new relational model which includes Reggia's model as a particular case and which all… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.1466v1-abstract-full').style.display = 'inline'; document.getElementById('1303.1466v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1303.1466v1-abstract-full" style="display: none;"> Relational models for diagnosis are based on a direct description of the association between disorders and manifestations. This type of model has been specially used and developed by Reggia and his co-workers in the late eighties as a basic starting point for approaching diagnosis problems. The paper proposes a new relational model which includes Reggia's model as a particular case and which allows for a more expressive representation of the observations and of the manifestations associated with disorders. The model distinguishes, i) between manifestations which are certainly absent and those which are not (yet) observed, and ii) between manifestations which cannot be caused by a given disorder and manifestations for which we do not know if they can or cannot be caused by this disorder. This new model, which can handle uncertainty in a non-probabilistic way, is based on possibility theory and so-called twofold fuzzy sets, previously introduced by the authors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1303.1466v1-abstract-full').style.display = 'none'; document.getElementById('1303.1466v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 March, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI1993)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1993-PG-106-113 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.6803">arXiv:1302.6803</a> <span> [<a href="https://arxiv.org/pdf/1302.6803">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> An Ordinal View of Independence with Application to Plausible Reasoning </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=del+Cerro%2C+L+F">Luis Farinas del Cerro</a>, <a href="/search/?searchtype=author&query=Herzig%2C+A">Andreas Herzig</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.6803v1-abstract-short" style="display: inline;"> An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.6803v1-abstract-full').style.display = 'inline'; document.getElementById('1302.6803v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.6803v1-abstract-full" style="display: none;"> An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, and a complete axiomatization is provided for the strongest one. Moreover we show that weak independence is well-suited to the problems of belief change and plausible reasoning, especially to address the problem of blocking of property inheritance in exception-tolerant taxonomic reasoning. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.6803v1-abstract-full').style.display = 'none'; document.getElementById('1302.6803v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1994-PG-195-203 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.4944">arXiv:1302.4944</a> <span> [<a href="https://arxiv.org/pdf/1302.4944">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Numerical Representations of Acceptance </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.4944v1-abstract-short" style="display: inline;"> Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of acceptance, what we call acceptance functions. Due to the monotonicity property of confidence measures, the acceptance of a proposition entails the acceptance of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.4944v1-abstract-full').style.display = 'inline'; document.getElementById('1302.4944v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.4944v1-abstract-full" style="display: none;"> Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of acceptance, what we call acceptance functions. Due to the monotonicity property of confidence measures, the acceptance of a proposition entails the acceptance of any of its logical consequences. In agreement with the idea that a belief set (in the sense of Gardenfors) must be closed under logical consequence, it is also required that the separate acceptance o two propositions entail the acceptance of their conjunction. Necessity (and possibility) measures agree with this view of acceptance while probability and belief functions generally do not. General properties of acceptance functions are estabilished. The motivation behind this work is the investigation of a setting for belief revision more general than the one proposed by Alchourron, Gardenfors and Makinson, in connection with the notion of conditioning. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.4944v1-abstract-full').style.display = 'none'; document.getElementById('1302.4944v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1995-PG-149-156 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.4936">arXiv:1302.4936</a> <span> [<a href="https://arxiv.org/pdf/1302.4936">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Practical Model-Based Diagnosis with Qualitative Possibilistic Uncertainty </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Cayrac%2C+D">Didier Cayrac</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.4936v1-abstract-short" style="display: inline;"> An approach to fault isolation that exploits vastly incomplete models is presented. It relies on separate descriptions of each component behavior, together with the links between them, which enables focusing of the reasoning to the relevant part of the system. As normal observations do not need explanation, the behavior of the components is limited to anomaly propagation. Diagnostic solutions are… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.4936v1-abstract-full').style.display = 'inline'; document.getElementById('1302.4936v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.4936v1-abstract-full" style="display: none;"> An approach to fault isolation that exploits vastly incomplete models is presented. It relies on separate descriptions of each component behavior, together with the links between them, which enables focusing of the reasoning to the relevant part of the system. As normal observations do not need explanation, the behavior of the components is limited to anomaly propagation. Diagnostic solutions are disorders (fault modes or abnormal signatures) that are consistent with the observations, as well as abductive explanations. An ordinal representation of uncertainty based on possibility theory provides a simple exception-tolerant description of the component behaviors. We can for instance distinguish between effects that are more or less certainly present (or absent) and effects that are more or less certainly present (or absent) when a given anomaly is present. A realistic example illustrates the benefits of this approach. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.4936v1-abstract-full').style.display = 'none'; document.getElementById('1302.4936v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1995-PG-68-76 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.3575">arXiv:1302.3575</a> <span> [<a href="https://arxiv.org/pdf/1302.3575">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Belief Revision with Uncertain Inputs in the Possibilistic Setting </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.3575v1-abstract-short" style="display: inline;"> This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal scale only, and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning. Besides, r… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.3575v1-abstract-full').style.display = 'inline'; document.getElementById('1302.3575v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.3575v1-abstract-full" style="display: none;"> This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal scale only, and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning. Besides, revision under uncertain inputs can be understood in two different ways depending on whether the input is viewed, or not, as a constraint to enforce. Moreover, it is shown that M.A. Williams' transmutations, originally defined in the setting of Spohn's functions, can be captured in this framework, as well as Boutilier's natural revision. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.3575v1-abstract-full').style.display = 'none'; document.getElementById('1302.3575v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1996-PG-236-243 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.3559">arXiv:1302.3559</a> <span> [<a href="https://arxiv.org/pdf/1302.3559">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Coping with the Limitations of Rational Inference in the Framework of Possibility Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Benferhat%2C+S">Salem Benferhat</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.3559v1-abstract-short" style="display: inline;"> Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does not provide expected results either because it cannot produce them, or even provide counter-intuitive conclusions. This state of facts is not due to the princip… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.3559v1-abstract-full').style.display = 'inline'; document.getElementById('1302.3559v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.3559v1-abstract-full" style="display: none;"> Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does not provide expected results either because it cannot produce them, or even provide counter-intuitive conclusions. This state of facts is not due to the principle of selecting a unique ordering of interpretations (which can be encoded by one possibility distribution), but rather to the absence of constraints expressing pieces of knowledge we have implicitly in mind. It is advocated in this paper that constraints induced by independence information can help finding the right ordering of interpretations. In particular, independence constraints can be systematically assumed with respect to formulas composed of literals which do not appear in the conditional knowledge base, or for default rules with respect to situations which are "normal" according to the other default rules in the base. The notion of independence which is used can be easily expressed in the qualitative setting of possibility theory. Moreover, when a counter-intuitive plausible conclusion of a set of defaults, is in its rational closure, but not in its preferential closure, it is always possible to repair the set of defaults so as to produce the desired conclusion. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.3559v1-abstract-full').style.display = 'none'; document.getElementById('1302.3559v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1996-PG-90-97 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1302.1537">arXiv:1302.1537</a> <span> [<a href="https://arxiv.org/pdf/1302.1537">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Decision-making Under Ordinal Preferences and Comparative Uncertainty </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Fargier%2C+H">Helene Fargier</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1302.1537v1-abstract-short" style="display: inline;"> This paper investigates the problem of finding a preference relation on a set of acts from the knowledge of an ordering on events (subsets of states of the world) describing the decision-maker (DM)s uncertainty and an ordering of consequences of acts, describing the DMs preferences. However, contrary to classical approaches to decision theory, we try to do it without resorting to any numerical re… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.1537v1-abstract-full').style.display = 'inline'; document.getElementById('1302.1537v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1302.1537v1-abstract-full" style="display: none;"> This paper investigates the problem of finding a preference relation on a set of acts from the knowledge of an ordering on events (subsets of states of the world) describing the decision-maker (DM)s uncertainty and an ordering of consequences of acts, describing the DMs preferences. However, contrary to classical approaches to decision theory, we try to do it without resorting to any numerical representation of utility nor uncertainty, and without even using any qualitative scale on which both uncertainty and preference could be mapped. It is shown that although many axioms of Savage theory can be preserved and despite the intuitive appeal of the method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty, but leads to the kind of uncertainty theory encountered in non-monotonic reasoning (especially preferential and rational inference), closely related to possibility theory. Moreover the method turns out to be either very little decisive or to lead to very risky decisions, although its basic principles look sound. This paper raises the question of the very possibility of purely symbolic approaches to Savage-like decision-making under uncertainty and obtains preliminary negative results. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1302.1537v1-abstract-full').style.display = 'none'; document.getElementById('1302.1537v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 February, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI1997)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1997-PG-157-164 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.7372">arXiv:1301.7372</a> <span> [<a href="https://arxiv.org/pdf/1301.7372">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Qualitative Decision Theory with Sugeno Integrals </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Sabbadin%2C+R">Regis Sabbadin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.7372v1-abstract-short" style="display: inline;"> This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding utility is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Technically speaking, Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. The axiomatic justification of Sugeno integ… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.7372v1-abstract-full').style.display = 'inline'; document.getElementById('1301.7372v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.7372v1-abstract-full" style="display: none;"> This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding utility is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Technically speaking, Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. The axiomatic justification of Sugeno integral-based utility is expressed in terms of preference between acts as in Savage decision theory. Pessimistic and optimistic qualitative utilities, based on necessity and possibility measures, previously introduced by two of the authors, can be retrieved in this setting by adding appropriate axioms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.7372v1-abstract-full').style.display = 'none'; document.getElementById('1301.7372v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1998-PG-121-128 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.7371">arXiv:1301.7371</a> <span> [<a href="https://arxiv.org/pdf/1301.7371">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Comparative Uncertainty, Belief Functions and Accepted Beliefs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Fargier%2C+H">Helene Fargier</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.7371v1-abstract-short" style="display: inline;"> This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical deductive closure and uncertain reasoning covers precisely the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and nothing else. In terms o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.7371v1-abstract-full').style.display = 'inline'; document.getElementById('1301.7371v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.7371v1-abstract-full" style="display: none;"> This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical deductive closure and uncertain reasoning covers precisely the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and nothing else. In terms of uncertain reasoning any possibility or necessity measure gives birth to a structure of accepted beliefs. The classes of probability functions and of Shafer's belief functions which yield belief sets prove to be very special ones. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.7371v1-abstract-full').style.display = 'none'; document.getElementById('1301.7371v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1998-PG-113-120 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.6692">arXiv:1301.6692</a> <span> [<a href="https://arxiv.org/pdf/1301.6692">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Assessing the value of a candidate. Comparing belief function and possibility theories </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Grabisch%2C+M">Michel Grabisch</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a>, <a href="/search/?searchtype=author&query=Smets%2C+P">Philippe Smets</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.6692v1-abstract-short" style="display: inline;"> The problem of assessing the value of a candidate is viewed here as a multiple combination problem. On the one hand a candidate can be evaluated according to different criteria, and on the other hand several experts are supposed to assess the value of candidates according to each criterion. Criteria are not equally important, experts are not equally competent or reliable. Moreover levels of satisf… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6692v1-abstract-full').style.display = 'inline'; document.getElementById('1301.6692v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.6692v1-abstract-full" style="display: none;"> The problem of assessing the value of a candidate is viewed here as a multiple combination problem. On the one hand a candidate can be evaluated according to different criteria, and on the other hand several experts are supposed to assess the value of candidates according to each criterion. Criteria are not equally important, experts are not equally competent or reliable. Moreover levels of satisfaction of criteria, or levels of confidence are only assumed to take their values in qualitative scales which are just linearly ordered. The problem is discussed within two frameworks, the transferable belief model and the qualitative possibility theory. They respectively offer a quantitative and a qualitative setting for handling the problem, providing thus a way to compare the nature of the underlying assumptions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6692v1-abstract-full').style.display = 'none'; document.getElementById('1301.6692v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1999-PG-170-177 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.6679">arXiv:1301.6679</a> <span> [<a href="https://arxiv.org/pdf/1301.6679">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Possibilistic logic bases and possibilistic graphs </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Benferhat%2C+S">Salem Benferhat</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Garcia%2C+L">Laurent Garcia</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.6679v1-abstract-short" style="display: inline;"> Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility dist… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6679v1-abstract-full').style.display = 'inline'; document.getElementById('1301.6679v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.6679v1-abstract-full" style="display: none;"> Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility distribution (which rank-orders the possible interpretations). A possibility distribution can be decomposed using a chain rule which may be based on two different kinds of conditioning which exist in possibility theory (one based on product in a numerical setting, one based on minimum operation in a qualitative setting). These two types of conditioning induce two kinds of possibilistic graphs. In both cases, a translation of these graphs into possibilistic bases is provided. The converse translation from a possibilistic knowledge base into a min-based graph is also described. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.6679v1-abstract-full').style.display = 'none'; document.getElementById('1301.6679v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-1999-PG-57-64 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.3835">arXiv:1301.3835</a> <span> [<a href="https://arxiv.org/pdf/1301.3835">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> A Principled Analysis of Merging Operations in Possibilistic Logic </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Benferhat%2C+S">Salem Benferhat</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Kaci%2C+S">Souhila Kaci</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.3835v1-abstract-short" style="display: inline;"> Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of merging operators are considered including conjunctive, disjunctive, reinforcement, adaptive and averaging operators. Then we propose to analyse these classes in t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.3835v1-abstract-full').style.display = 'inline'; document.getElementById('1301.3835v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.3835v1-abstract-full" style="display: none;"> Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of merging operators are considered including conjunctive, disjunctive, reinforcement, adaptive and averaging operators. Then we propose to analyse these classes in terms of postulates. This is done by first extending the postulate for merging classical bases to the case where priorites are avaialbe. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.3835v1-abstract-full').style.display = 'none'; document.getElementById('1301.3835v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-2000-PG-24-31 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.2255">arXiv:1301.2255</a> <span> [<a href="https://arxiv.org/pdf/1301.2255">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Graphical readings of possibilistic logic bases </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Benferhat%2C+S">Salem Benferhat</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Kaci%2C+S">Souhila Kaci</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.2255v1-abstract-short" style="display: inline;"> Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the conditioning is either based on the minimum, or the product operator. Benferhat et al. (1999) have investigated the connections between min-based graphs and poss… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.2255v1-abstract-full').style.display = 'inline'; document.getElementById('1301.2255v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.2255v1-abstract-full" style="display: none;"> Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the conditioning is either based on the minimum, or the product operator. Benferhat et al. (1999) have investigated the connections between min-based graphs and possibilistic logic bases (made of classical formulas weighted in terms of certainty). This paper deals with a more difficult issue : the product-based graphical representations of possibilistic bases, which provides an easy structural reading of possibilistic bases. Moreover, this paper also provides another reading of possibilistic bases in terms of comparative preferences of the form "in the context p, q is preferred to not q". This enables us to explicit preferences underlying a set of goals with different levels of priority. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.2255v1-abstract-full').style.display = 'none'; document.getElementById('1301.2255v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 January, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI2001)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-2001-PG-24-31 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1301.0555">arXiv:1301.0555</a> <span> [<a href="https://arxiv.org/pdf/1301.0555">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Bipolar Possibilistic Representations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Benferhat%2C+S">Salem Benferhat</a>, <a href="/search/?searchtype=author&query=Dubois%2C+D">Didier Dubois</a>, <a href="/search/?searchtype=author&query=Kaci%2C+S">Souhila Kaci</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1301.0555v1-abstract-short" style="display: inline;"> Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be useful when representing knowledge, for modelling values which are not impossible because they are consistent with the available knowledge on the one hand, and v… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.0555v1-abstract-full').style.display = 'inline'; document.getElementById('1301.0555v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1301.0555v1-abstract-full" style="display: none;"> Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be useful when representing knowledge, for modelling values which are not impossible because they are consistent with the available knowledge on the one hand, and values guaranteed to be possible because reported from observations on the other hand. It is also of interest when expressing preferences, to point out values which are positively desired among those which are not rejected. This distinction can be encoded by two types of constraints expressed in terms of necessity measures and in terms of guaranteed possibility functions, which induce a pair of possibility distributions at the semantic level. A consistency condition should ensure that what is claimed to be guaranteed as possible is indeed not impossible. The present paper investigates the representation of this bipolar view, including the case when it is stated by means of conditional measures, or by means of comparative context-dependent constraints. The interest of this bipolar framework, which has been recently stressed for expressing preferences, is also pointed out in the representation of diagnostic knowledge. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1301.0555v1-abstract-full').style.display = 'none'; document.getElementById('1301.0555v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 December, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI2002)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-2002-PG-45-52 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1207.4130">arXiv:1207.4130</a> <span> [<a href="https://arxiv.org/pdf/1207.4130">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> Using arguments for making decisions: A possibilistic logic approach </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Amgoud%2C+L">Leila Amgoud</a>, <a href="/search/?searchtype=author&query=Prade%2C+H">Henri Prade</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1207.4130v1-abstract-short" style="display: inline;"> Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision making process, there have been few formal proposals handling this idea if we except works by Fox and Parsons and by Bonet and Geffner. In this paper we propose… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1207.4130v1-abstract-full').style.display = 'inline'; document.getElementById('1207.4130v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1207.4130v1-abstract-full" style="display: none;"> Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision making process, there have been few formal proposals handling this idea if we except works by Fox and Parsons and by Bonet and Geffner. In this paper we propose a possibilistic logic framework where arguments are built from an uncertain knowledge base and a set of prioritized goals. The proposed approach can compute two kinds of decisions by distinguishing between pessimistic and optimistic attitudes. When the available, maybe uncertain, knowledge is consistent, as well as the set of prioritized goals (which have to be fulfilled as far as possible), the method for evaluating decisions on the basis of arguments agrees with the possibility theory-based approach to decision-making under uncertainty. Taking advantage of its relation with formal approaches to defeasible argumentation, the proposed framework can be generalized in case of partially inconsistent knowledge, or goal bases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1207.4130v1-abstract-full').style.display = 'none'; document.getElementById('1207.4130v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 July, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UAI-P-2004-PG-10-17 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 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