{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T00:05:21Z","timestamp":1752192321626,"version":"3.41.2"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T00:00:00Z","timestamp":1704758400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We investigate degree of satisfiability questions in the context of Heyting algebras and intuitionistic logic. We classify all equations in one free variable with respect to finite satisfiability gap, and determine which common principles of classical logic in multiple free variables have finite satisfiability gap. In particular we prove that, in a finite non-Boolean Heyting algebra, the probability that a randomly chosen element satisfies <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481224000021_inline1.png\"\/><jats:tex-math>\n$x \\vee \\neg x = \\top $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is no larger than <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0022481224000021_inline2.png\"\/><jats:tex-math>\n$\\frac {2}{3}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Finally, we generalize our results to infinite Heyting algebras, and present their applications to point-set topology, black-box algebras, and the philosophy of logic.<\/jats:p>","DOI":"10.1017\/jsl.2024.2","type":"journal-article","created":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T03:40:30Z","timestamp":1704771630000},"page":"533-551","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["DEGREE OF SATISFIABILITY IN HEYTING ALGEBRAS"],"prefix":"10.1017","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8686-2319","authenticated-orcid":false,"given":"BENJAMIN MERLIN","family":"BUMPUS","sequence":"first","affiliation":[]},{"given":"ZOLTAN A.","family":"KOCSIS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,1,9]]},"reference":[{"key":"S0022481224000021_r18","first-page":"208","article-title":"On the extension of the intuitionist propositional calculus to the classical calculus, and the minimal calculus to the intuitionist calculus (in Russian)","volume":"32","author":"Yankov","year":"1968","journal-title":"Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya"},{"key":"S0022481224000021_r5","first-page":"115","volume-title":"Mathematical Software \u2013 ICMS 2020","volume":"2020","author":"Borovik"},{"volume-title":"Distributive Lattices","year":"1975","author":"Balbes","key":"S0022481224000021_r3"},{"key":"S0022481224000021_r16","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1007\/s10992-015-9360-z","article-title":"The justification of the basic laws of logic","volume":"44","author":"Russell","year":"2015","journal-title":"Journal of Philosophical Logic"},{"key":"S0022481224000021_r14","doi-asserted-by":"crossref","unstructured":"[14] Pitts, A. 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