Horn clause from FOLDOC

<!DOCTYPE html> <html lang="en"> <head> <title>Horn clause from FOLDOC</title> <meta http-equiv="Content-Security-Policy" content="default-src 'unsafe-inline' http: https:"> <meta name="verify-v1" content="siAI0ZOMn41hao0E/T76D1I2L3MtFjzE48P3ctCjRNU="> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="msapplication-TileColor" content="#da532c"> <meta name="theme-color" content="#ffffff"> <meta name="google-translate-customization" content="828219db36930e1e-c51d915bf2ea717c-g9b503f9a85d5b5a7-a">  <script src="https://www.googletagmanager.com/gtag/js?id=UA-9715943-1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-9715943-1'); </script>  <link href="//fonts.googleapis.com/css?family=Duru+Sans%7CBelgrano%7CInconsolata%7CAlef%7CArmata" rel="stylesheet" type="text/css"> <link rel="stylesheet" type="text/css" href="/css/layout.css?2">  <link rel="apple-touch-icon" sizes="152x152" href="/im/apple-touch-icon.png"> <link rel="icon" type="image/png" sizes="32x32" href="/im/favicon-32x32.png"> <link rel="icon" type="image/png" sizes="16x16" href="/im/favicon-16x16.png"> <link rel="manifest" href="/im/site.webmanifest"> <link rel="mask-icon" href="/im/safari-pinned-tab.svg" color="#5bbad5"> <link rel="canonical" href="https://foldoc.org/Horn+clause"> <link rel="alternate" type="application/rss+xml" title="FOLDOC" href="/rss.xml"> <link rel="search" title="FOLDOC" type="application/opensearchdescription+xml" href="//foldoc.org/search.xml">  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-5521724329338202" crossorigin="anonymous"></script>  </head> <body> <div id="fb-root"></div> <script> (function (d, s, id) { var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) return; js = d.createElement(s); js.id = id; js.src = "//connect.facebook.net/en_GB/all.js#xfbml=1"; fjs.parentNode.insertBefore(js, fjs); }(document, 'script', 'facebook-jssdk')); </script> <div id="container"> <div id="left"> <a href="/"> <img src="/foldoc.gif" width="300" height="98" alt="Free On-line Dictionary of Computing" class="logo"> </a> <div id="nav"> <a href="/contents.html" class="button">Contents</a> <a href="/help.html" class="button">Help</a> <a href="/random-entry" class="button">Random</a> </div> <form action="/"> <input type="text" name="query" id="query" autofocus="autofocus"> <input type="submit" name="action" value="Search" class="button"> </form> <div id="content"> <h2>Horn clause</h2> <p></p> <p><<i><a href="contents/logic.html">logic</a></i>></p> <p> A set of <a href="/atomic+literals">atomic literals</a> with at most one <a href="/positive+literal">positive literal</a>. Usually written <p></p> <pre> L <- L1, ..., Ln </pre>or <pre> <- L1, ..., Ln </pre>where n>=0, "<-" means "is implied by" and comma stands for <a href="/conjuction">conjuction</a> ("AND"). If L is false the clause is regarded as a <a href="/goal">goal</a>. Horn clauses can express a subset of statements of <a href="/first+order+logic">first order logic</a>. <p></p> The name "Horn Clause" comes from the logician Alfred Horn, who first pointed out the significance of such clauses in 1951, in the article "On sentences which are true of direct unions of algebras", Journal of Symbolic Logic, 16, 14-21. <p></p> A <a href="/definite+clause">definite clause</a> is a Horn clause that has exactly one positive literal. <p></p> <p class="updated">Last updated: <a href="/new.html">2000-01-24</a></p> <p></p> <p class="vertical-space"></p><h3>Nearby terms:</h3> <p class="neighbours"> <a href="/horizontal+scan+rate">horizontal scan rate</a> &diams; <a href="/horizontal+tabulation">horizontal tabulation</a> &diams; <b><a href="/Horn+clause">Horn clause</a></b> &diams; <a href="/hose">hose</a> &diams; <a href="/hosed">hosed</a> </p> <p> Try this search on <a href="https://www.wikipedia.org/wiki/Special:Search?search=Horn+clause">Wikipedia</a>, <a href="https://www.wiktionary.org/wiki/Horn+clause">Wiktionary</a>, <a href="https://www.google.com/search?q=define:Horn+clause">Google</a>, <a href="https://www.onelook.com/?w=Horn+clause">OneLook</a>. </p> <p class="vertical-space"></p> <hr> <div></div> <hr>  <div id="HCB_comment_box">Loading</div> <link rel="stylesheet" type="text/css" href="//www.htmlcommentbox.com/static/skins/bootstrap/twitter-bootstrap.css?v=0"> <script language="javascript" id="hcb"> hcb_user = { PAGE: 'https://foldoc.org/Horn+clause', comments_header: ' ', no_comments_msg: ' ', err_comment_empty: 'Your comment was not posted because it was empty!', rss: '', }; var s = document.createElement("script"); s.setAttribute("type", "text/javascript"); s.setAttribute("src", "//www.htmlcommentbox.com/jread?page=" + escape(hcb_user.PAGE).replace(/\+/g, "%2B") + "&mod=%241%24wq1rdBcg%24.0y2uzvjA2bsnhzpXVq9F." + "&opts=17374&num=10"); // No e-mail field: 16846 if (typeof s != "undefined") document.getElementsByTagName("head")[0].appendChild(s); </script> <script> setTimeout(function () { document.getElementById('hcb_form_content').rows = 1 }, 1000); </script> <hr>  </div>  </div>  <div id="right"> <div id="google_translate_element"> <script> function googleTranslateElementInit() { new google.translate.TranslateElement({ pageLanguage: 'en' }, 'google_translate_element'); } </script> <script src="https://translate.google.com/translate_a/element.js?cb=googleTranslateElementInit"></script> </div> <p><br></p> <hr> <div id="social"> <div class="fb-like" data-href="http://foldoc.org/" data-layout="button_count" data-action="like" data-show-faces="false" data-share="true"> </div> <a href="https://twitter.com/share" class="twitter-share-button" data-via="foldoc"> Tweet </a> <script> if (!document.getElementById('twitter-wjs')) { var fjs = document.getElementsByTagName('script')[0], js = document.createElement('script'); js.id = 'twitter-wjs'; js.src = 'https://platform.twitter.com/widgets.js'; fjs.parentNode.insertBefore(js, fjs); } </script> </div> <hr> <div> <p></p> </div> <p> <a href="/rss.xml"> <img src="/orangerss.gif" width="14" height="14" alt="RSS feed of new items"> </a>   <a href="/new.html">Recent Updates</a>     |     <a href="/missing.html">Missing Terms</a> </p> <p>Updated: Tue, 11 Feb 2025 23:28:55 GMT</p> <p>15282 entries</p> <p><em><a href="/Free+On-line+Dictionary">Copyright Denis Howe 1985</a></em></p> </div>  </div>   <script type="text/javascript"> window._qevents = window._qevents || []; (function() { var elem = document.createElement('script'); elem.src = 'https://secure.quantserve.com/quant.js'; elem.async = true; elem.type = 'text/javascript'; var scpt = document.getElementsByTagName('script')[0]; scpt.parentNode.insertBefore(elem, scpt); })(); window._qevents.push({ qacct: 'p-48Rosdvs3EiOc', uid: '__INSERT_EMAIL_HERE__' }); </script> <noscript> <div style="display:none;"> <img src="https//pixel.quantserve.com/pixel/p-48Rosdvs3EiOc.gif" border="0" height="1" width="1" alt="Quantcast"/> </div> </noscript>  </body> </html>

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Horn clause from FOLDOC