{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T01:58:53Z","timestamp":1713405533824},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T00:00:00Z","timestamp":1694390400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,4,19]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We introduce dual counterpart intuitionistic logic (or DCInt): a constructive logic that is a conservative extension of intuitionistic logic, a sublogic of bi-intuitionistic logic, has the logical duality property of classical logic, and also retains the modal character of its interpretation of the connective dual to intuitionistic implication. We define its Kripke semantics along with the corresponding notion of a bisimulation, and then prove that it has both the disjunction property and (its dual) the constructible falsity property. Also, for any class $ {\\mathcal{C}}$ of Kripke frames from our semantics, we identify a condition such that $ {\\mathcal{C}}$ will have the disjunction property if it satisfies the condition. This provides a method for generating extensions of DCInt that retain the disjunction property.<\/jats:p>","DOI":"10.1093\/logcom\/exad019","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T11:22:10Z","timestamp":1694517730000},"page":"590-634","source":"Crossref","is-referenced-by-count":0,"title":["Dual counterpart intuitionistic logic"],"prefix":"10.1093","volume":"34","author":[{"given":"Anthony","family":"Cantor","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Iowa , Iowa City, IA, USA"}]},{"given":"Aaron","family":"Stump","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Iowa , Iowa City, IA, USA"}]}],"member":"286","published-online":{"date-parts":[[2023,9,11]]},"reference":[{"key":"2024041707214696900_ref1","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1007\/s11225-016-9664-1","article-title":"Bi-simulating in bi-intuitionistic logic","volume":"104","author":"Badia","year":"2016","journal-title":"Studia Logica"},{"key":"2024041707214696900_ref2","volume-title":"Modal Correspondence Theory","author":"van Benthem","year":"1976"},{"key":"2024041707214696900_ref3","volume-title":"Modal Logic: Graph. Darst","author":"Blackburn","year":"2002"},{"key":"2024041707214696900_ref4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.jal.2004.07.016","article-title":"Anti-intuitionism and paraconsistency","volume":"3","author":"Brunner","year":"2005","journal-title":"Journal of Applied Logic"},{"key":"2024041707214696900_ref5","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1007\/s11225-014-9596-6","article-title":"The semi Heyting\u2013Brouwer logic","volume":"103","author":"Cornejo","year":"2015","journal-title":"Studia Logica"},{"key":"2024041707214696900_ref6","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0304-3975(99)00124-3","article-title":"Subtractive logic","volume":"254","author":"Crolard","year":"2001","journal-title":"Theoretical Computer Science"},{"key":"2024041707214696900_ref7","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1145\/357766.351262","article-title":"The duality of computation","volume":"35","author":"Curien","year":"2000","journal-title":"ACM Sigplan Notices"},{"key":"2024041707214696900_ref8","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1305\/ndjfl\/1093888021","article-title":"A remark on Gentzen\u2019s calculus of sequents","volume":"18","author":"Czermak","year":"1977","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2024041707214696900_ref9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02962-6","volume-title":"Logic and Structure","author":"van Dalen","year":"1994"},{"key":"2024041707214696900_ref10","volume-title":"Sequent Calculus: A Logic and a Language for Computation and Duality","author":"Downen","year":"2017"},{"key":"2024041707214696900_ref11","article-title":"Duality in action (invited talk)","volume-title":"6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)","author":"Downen","year":"2021"},{"key":"2024041707214696900_ref12","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1093\/logcom\/exz010","article-title":"A bilateral hilbert-style investigation of 2-intuitionistic logic","volume":"29","author":"Drobyshevich","year":"2019","journal-title":"Journal of Logic and Computation"},{"key":"2024041707214696900_ref13","article-title":"Moisil\u2019s modal logic and related systems","volume-title":"Relevance Logics and Other Tools for Reasoning. Essays in Honour of Michael Dunn","author":"Drobyshevich","year":"2022"},{"key":"2024041707214696900_ref14","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1026740726955","article-title":"Partiality and its dual","volume":"66","author":"Dunn","year":"2000","journal-title":"Studia Logica"},{"key":"2024041707214696900_ref15","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s11225-013-9469-4","article-title":"Extensions of Priest\u2013Da Costa logic","volume":"102","author":"Ferguson","year":"2014","journal-title":"Studia Logica"},{"key":"2024041707214696900_ref16","first-page":"1945","article-title":"Axiomatic classes of intuitionistic models","volume":"11","author":"Goldblatt","year":"2005","journal-title":"Journal of Universal Computer Science"},{"key":"2024041707214696900_ref17","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1002\/malq.19810270803","article-title":"The logic of contradiction","volume":"27","author":"Goodman","year":"1981","journal-title":"Mathematical Logic Quarterly"},{"key":"2024041707214696900_ref18","first-page":"269","article-title":"Bi-intuitionistic logics: a new instance of an old problem","author":"Gor\u00e9","year":"2020","journal-title":"In AiML"},{"key":"2024041707214696900_ref19","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/978-3-662-59533-6_10","article-title":"Hennessy\u2013Milner properties for (modal) bi-intuitionistic logic","volume-title":"International Workshop on Logic, Language, Information, and Computation","author":"de Groot","year":"2019"},{"key":"2024041707214696900_ref20","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF02121114","article-title":"Intuitionistic logic with strong negation","volume":"36","author":"Gurevich","year":"1977","journal-title":"Studia Logica"},{"key":"2024041707214696900_ref21","doi-asserted-by":"crossref","DOI":"10.4324\/9780203290644","volume-title":"A New Introduction to Modal Logic","author":"Hughes","year":"1996"},{"key":"2024041707214696900_ref22","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1093\/logcom\/7.4.501","article-title":"Simulating without negation","volume":"7","author":"Kurtonina","year":"1997","journal-title":"Journal of Logic and Computation"},{"key":"2024041707214696900_ref23","first-page":"187","article-title":"Konstruktivnaja logika","volume":"5","author":"Markov","year":"1950","journal-title":"Uspekhi Matematicheskikh Nauk"},{"key":"2024041707214696900_ref24","doi-asserted-by":"crossref","first-page":"16","DOI":"10.2307\/2268973","article-title":"Constructible falsity","volume":"14","author":"Nelson","year":"1949","journal-title":"The Journal of Symbolic Logic"},{"key":"2024041707214696900_ref25","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/3-540-63141-0_24","article-title":"Bisimulation and propositional intuitionistic logic","volume-title":"International Conference on Concurrency Theory","author":"Patterson","year":"1997"},{"key":"2024041707214696900_ref26","first-page":"165","article-title":"Dualising intuitionistic negation","volume":"13","author":"Priest","year":"2009","journal-title":"Principia: An International Journal of Epistemology"},{"key":"2024041707214696900_ref27","volume-title":"An Algebraic and Kripke-Style Approach to a Certain Extension of Intuitionistic Logic","author":"Rauszer","year":"1980"},{"key":"2024041707214696900_ref28","first-page":"199","article-title":"The semantics of entailment","volume-title":"Studies in Logic and the Foundations of Mathematics","author":"Routley","year":"1973"},{"key":"2024041707214696900_ref29","doi-asserted-by":"crossref","DOI":"10.4204\/EPTCS.243.8","article-title":"Strong completeness and the finite model property for bi-intuitionistic stable tense logics","author":"Sano","year":"2017"},{"key":"2024041707214696900_ref30","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1002\/malq.19690151602","article-title":"A semantical study of constructible falsity","volume":"15","author":"Thomason","year":"1969","journal-title":"Mathematical Logic Quarterly"},{"key":"2024041707214696900_ref31","doi-asserted-by":"crossref","first-page":"S72","DOI":"10.1016\/j.jal.2017.12.001","article-title":"Natural deduction for bi-intuitionistic logic","volume":"25","author":"Tranchini","year":"2017","journal-title":"Journal of Applied Logic"},{"key":"2024041707214696900_ref32","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1305\/ndjfl\/1039886520","article-title":"Dual-intuitionistic logic","volume":"37","author":"Urbas","year":"1996","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2024041707214696900_ref33","first-page":"426","article-title":"Halld\u00e9n-completeness by gluing of Kripke frames","volume":"24","author":"Van Benthem","year":"1983","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2024041707214696900_ref34","doi-asserted-by":"crossref","first-page":"341","DOI":"10.3166\/jancl.18.341-364","article-title":"Constructive negation, implication, and co-implication","volume":"18","author":"Wansing","year":"2008","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"2024041707214696900_ref35","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1093\/logcom\/ext035","article-title":"Falsification, natural deduction and bi-intuitionistic logic","volume":"26","author":"Wansing","year":"2016","journal-title":"Journal of Logic and Computation"},{"key":"2024041707214696900_ref36","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.jal.2017.01.002","article-title":"A more general general proof theory","volume":"25","author":"Wansing","year":"2017","journal-title":"Journal of Applied Logic"},{"key":"2024041707214696900_ref37","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.apal.2008.01.001","article-title":"On the unity of duality","volume":"153","author":"Zeilberger","year":"2008","journal-title":"Annals of Pure and Applied Logic"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/34\/3\/590\/57242188\/exad019.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/34\/3\/590\/57242188\/exad019.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T18:31:08Z","timestamp":1713378668000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/34\/3\/590\/7263234"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,11]]},"references-count":37,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,9,11]]},"published-print":{"date-parts":[[2024,4,19]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exad019","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,4]]},"published":{"date-parts":[[2023,9,11]]}}}