CINXE.COM
Just a moment...
<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMiIgaGVpZ2h0PSIzMiIgZmlsbD0ibm9uZSI+PHBhdGggZmlsbD0iI0IyMEYwMyIgZD0iTTE2IDNhMTMgMTMgMCAxIDAgMTMgMTNBMTMuMDE1IDEzLjAxNSAwIDAgMCAxNiAzbTAgMjRhMTEgMTEgMCAxIDEgMTEtMTEgMTEuMDEgMTEuMDEgMCAwIDEtMTEgMTEiLz48cGF0aCBmaWxsPSIjQjIwRjAzIiBkPSJNMTcuMDM4IDE4LjYxNUgxNC44N0wxNC41NjMgOS41aDIuNzgzem0tMS4wODQgMS40MjdxLjY2IDAgMS4wNTcuMzg4LjQwNy4zODkuNDA3Ljk5NCAwIC41OTYtLjQwNy45ODQtLjM5Ny4zOS0xLjA1Ny4zODktLjY1IDAtMS4wNTYtLjM4OS0uMzk4LS4zODktLjM5OC0uOTg0IDAtLjU5Ny4zOTgtLjk4NS40MDYtLjM5NyAxLjA1Ni0uMzk3Ii8+PC9zdmc+);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '9135704768859d18',cH: 'uxTqrBXr0a6WJGciurDA2AoPaV9Ghz1bCkDds2rIaZc-1739791755-1.2.1.1-.Cfp4IeTgbLSICht5NXQdwWI9SMDxJ91R8fUopscyhPasJMgKQvrEm5q1.S7uE5O',cUPMDTk: "\/abstracts\/search?q=mathematical%20reasoning&__cf_chl_tk=QPe_w4KpYvC6z.gFBH5h0vZQd1feldSCU_kZHMDsHMM-1739791755-1.0.1.1-hzwUUbmjWSs.JEq2N16A_gkGFxZZDTVlt1cOUQhB6YQ",cFPWv: 'b',cITimeS: '1739791755',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=mathematical%20reasoning&__cf_chl_f_tk=QPe_w4KpYvC6z.gFBH5h0vZQd1feldSCU_kZHMDsHMM-1739791755-1.0.1.1-hzwUUbmjWSs.JEq2N16A_gkGFxZZDTVlt1cOUQhB6YQ",md: "96IIIvRM3tegQXAn3Qtk4v.fPrAWQ5EjIGyu8NrMp70-1739791755-1.2.1.1-pDnQvZYxVDWlWS.6rhSGYibGU9KxCJMnPndjg.HiaLv2ypoBjshGUAeIws3qgoQlb00IISaeq9Ckpq63LNyPh5vYJ_00BJiykKdaftCm.cpsPe3wSbO.rm0sLeKd2Y03AuUUcNjD..WaababsCZbu6hXbcCWrn7qzElUubgxN99lvWSQT4EDVHsO6nwUKR4w3GEy1Lg10gGiz6MIST3B2HW7BFHZDaYTEnLKo_pKJgbNtSf2HgQT0w4tV_.wPrkWX6AIAotnoEvK99YYIlVRqsmmzm.ygIOxTjERrupG9OhKE68_CTsPDs6v57IJaDJzoFml_86AbMRFWym_il7Frd6eUZ6SK4z_Si7RA5Od7tOCPUiVSdpg5GnOt7lDmfXVXh8wNoo.AKjSbyc96Z8lyw3ffjrfFpO.cIWGb1FVrjFWaJgTYVsabqitwJksWrmmgduJhjDpY7VDwqiIc9nkC5QJmb0qJ8l_E4ZBeYpwWjSI.sPVrSc1GBK5Xxiz6sSczkOJXF3JpQu.svEXJrgsE8R6Qq.uPOEdnbl_84K0_Ckdol7he.HWRvVGxj6p9l2vrecdnukZR_aL6qdhY6O.8YJK72If6rINsccE7BKqm3M0AW_LF8b0mfu9bwwn4_yk7jgCSs6CHMVjD1qeJgAgzWH0yWdcNJ77YJXha0MbCquI77hiyz0IZ6a8vYLm_cusZFlUlyLYkBe4Hp4n5akQy8ucl3TKbAkfq2AuntvVnIZbm5qgV7ueF10ycRUU6zHrt1vO3Sr0jHqO6fsN4cFyKf7eO5jRTqrpAYo1RoCORDbvbBY3sKuE3dwU3h1flMYpUw3XeQPS8giAsOkDn69tkZVqr48pXu4wflhVYYDBrbA5I8J4zxz5WMDXNmLqtW2P6AjzIZvBMOQw_44kHypkKgJM1xykFncngTkbJ0p0k66DEIWUVaVxi9HZq6WlyvyjfACyAQ7E_5r6Sc3Mftooi2b6MKQwqJg2qKM0G_X8.WB3PdwTH6UPnRpYZRsMNqWn.L0_mdzek5aDoiBAGYBbxw0MIVlUg7ULpkxFqEtzzm7pfMmqcnnvebqS8hFTMjij_ZST1Jn8oJxjCFiKykDSI5TcDhdTE1.KzqkMHMW98VN9x5EHHRwoP.YIcbG1SbZ_3GZdDj_IBvSLxKpZKqsyh65edjQs0MFRqpGUIFbpBXIkpl_nNpkX35Dd69dC7.t.vdl8kRPIsuB3pb7vwru.3GySTMZLuBWqraZvBbmDwg73ji9kl9zzFUKF.mcLOmcHqqpoK2lEivD9DkEQTKtuh.B6nqBgUXJ3ANWv2U4Iyvtcm617s.4nCRFX.ivoXagbOqL3Rzn6Z3u01j.3frQHNKbg5q8LIzOvaG8P.9jDHVe6dKKHPRwGujPZ09lq_c0mCl01iP4I_doj1oomqY1KUT6EQvzMgxKHgr5r6uxvNpRyzzkFEFR0M5TpDMAeWHigbxJpHP5n_0DXPyFmsci8Ao_7gAfS6PRxyUNdSKyWTPljEDDXZs6U2S8KEXd11GSOXYFy8vHhWLdoqkYUxYiSGkaAqCbpBwiwFv1r6z6DKHrPRyJ_sFAJvUW1UdHliYhJc7GPYXOd0CXF7WNzzlr5Jf2rFtBVLIG5DSx_aXaB0YjA06Z0iUEQCGCoLPdVJMHNCPjrg5p8Bd9DhdjH7RO.Bh7HkhKwBypoXrvJp4StxvCeKpVBsgyxK7QdcGbvregbjkAA3z7oDIOn16nXkasMWBguCJg7m.u09xmdE9Z1B0zJOeVIRVvrYKDfQOqoWjiBrFd6L0RIROCXHwLTHdDClNhykocklTe4ytvBygY0sQVRlFGRCe_iM4rW3t0MU_pslGBQJaAu9uNOpygFX6MnXpedLInrGN28Z2G.j4Y_mv06wOeDe97aOfWf22yJRTnj6aPYDuqbG0ZWuAqx43lZuTue8uJPDNZH60FGuZ11jS4frx2IeBQaiYmykieeGtJ9",mdrd: "BxiGw7TybISo.Qb5aGQ6Rr4pbaqS.iflHjS2EoSyYcs-1739791755-1.2.1.1-Rf0pcJiZ46IH_D4kwNt36QrAs6D7AVI3osMQzYdd05mEBP._H5nX9zSeuZVcTOgYVex9mTlprxKxp8SerrKlXBOJ9bxRfJyIGhjTuqxwVmP58lK8s2WIfUYrvTOHAwT.xMoJsegKg_L5CU34dbbxE2lNQ2lWYksXanF5NwxM8zP7A.u_EkxAtQIMYvm1VowkW03D27fkODckMN2QSKecQoOqRp4VMLzgWcr.GRS6d2eEZ0PsYsGjmEjPc4Ogz6yz2u7RvyoMrLgY8Mr4DFpw3SwCZlQn3M0EriClRYLiHeENKCMWjVYiswc9n3ZaHHnWTPgQI5_LQYHbBfQE33yyMeuv.jVqmA6voBzuD1ShQab0qiL1FiP8_KCbiassDXi0H1NSh_LoKQ24XoGwK9OKAyK5CxdpX2ynqEYVFjYMZKcLjQO1X.5KxZXCtHzVHSGFfdJcRe4U6hGNHnqRNbvhv2uyuVGU.SNRkU8hybPPXCDD1KAwrX18wy2s0oiBSjh5AYCYJpJ8NE7g_C3oABuBpYsheEngXkH4rVjM5z_3BTxaChuXExPEBcZgGiULI7WF2y5ISevvHFEWPSspHMjSOHmzK0_jK69RVDsNSqjMyOvM1kPfBggNvl1YQfRkP_y7rMabbyEQr1i54.ZIodIC_frJGrmbMNtQ67jlXu35QW16T.aGbfEuEiqWp65q0ihzaPnjvELYw55joMwzX5tJpuw3bwcmDSV55W6Pn1aN6rXstGHjuyc8YQ5AG6eT6SJPN60mAu5F8C_v71jvVqza4EKS00mJtGjCvDKcBEug0ghjx3tCQhYH2bzgVMjW2ERwRAX_C.rK90J4ta5R2ZUDqT.d9_9.y_SbRjXZnH2AINhGyP5KVFObBMuQ1NtURdiPRdxZy4WSR.hgvZH.JHpvP.zuePri2.ohzrMf2TAkppKUYL.2HVUjs1tdBZ4vDX3OCsF8PHzwAqKdxrJ0BY3mUBP4bWfK1GaAg3vJAn3FdNOcviilKZynQAPwiToyj_KgrjGyG4Txs2MdcLquN6.hJpPwjn9Gzylcsa6TyXKBjMGMozPz0XuWth4Rq23XSd5KHAvcCdDh7gT8gmlorrZJcdeqTSw0OSyPcoKNhPVndNaSu_jJwluN.Y0dhi1ulCqSjhsTpH_V0FCWSK.pfOVjDgZabEDv5qUH6zdcN99KHDFW5Q5sUuPUTGolmwlzoug8APJ56bvJeiVSnBhsMs8LmNh300RFxeRF3DfNX9F_x0tfcUqHPmlZIG453Kev7tpV_tq5Ef.Z_CxlEgweXPaO2dyyl4JJWB6pRCNTqSwT5y5uRxM1A84azoHtOdu5x4t8ZCoa00AasD5HH6ljLHOkCoZB2lJgp9tnaz.sYbvKNlzunGREPmyToqqNkrqn79txSyR8WD0YSijjSIg8pX.fC18tWbZu.zuFzE7Ad5mdgj.6bPqi2hfJ.es4G1paCpICFhJF727eBtVbQmjsqBvvTAHLbEbkGSSLsxInZImMcMHTw6eGg37rH.dZEMBgQsjfGyJKCiDul_ICkweZtEAU8TGOrUoD3N4ZAqxNYzvMcMlfc9gy2Q0wterOjQINfcrdtKVDTV3cXVSnw7kMUmenRdu6LOLpCbuO6beFQmFffQ2U4AViQi5pPjriy4emZEtiMeZiAOk95vcpgEcGa3wLjx1_YP4DfljvWwqnzAuaSZr2mUIExBSJY_NlfMbzmipB3j9ZTFngCRhoC_l34i9o9pZM9ZzpUXNdCoGwwzpPV6OGCwWt31RQUgAcLQhJYVLXEqe7ZZzPXnX3WZHJSOqiqyxY01zGsL73tH3arOHzDeb6gFulYb01R1R.dnkoMHFHZoTtJO6xMS92Rm5PKKo1CnLInUcPDRc4yvwOd_leQ.D7gW_s4DyvpMii8nchHsBgZc6hRrmanuFfiOMkj_4Uog4cdGlpbusAFKYVsZgKcXZzadxMKBe_qcuY9XomyeH4"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=9135704768859d18';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=mathematical%20reasoning&__cf_chl_rt_tk=QPe_w4KpYvC6z.gFBH5h0vZQd1feldSCU_kZHMDsHMM-1739791755-1.0.1.1-hzwUUbmjWSs.JEq2N16A_gkGFxZZDTVlt1cOUQhB6YQ" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>