{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:37:17Z","timestamp":1740141437943,"version":"3.37.3"},"reference-count":45,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T00:00:00Z","timestamp":1613606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["19-78-00044"],"award-info":[{"award-number":["19-78-00044"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,1,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch\u2019s ${\\mathbf{S}_{\\mathbf{fde}}}$ and Szmuc\u2019s $\\mathbf{dS}_{\\mathbf{fde}}$. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both ${\\mathbf{S}_{\\mathbf{fde}}}$ and $\\mathbf{dS}_{\\mathbf{fde}}$ are formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for ${\\mathbf{S}_{\\mathbf{fde}}}$ containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for $\\mathbf{dS}_{\\mathbf{fde}}$ and to reflect the fundamental symmetry between ${\\mathbf{S}_{\\mathbf{fde}}}$ and $\\mathbf{dS}_{\\mathbf{fde}}$ on proof-theoretical level forming a convenient basis for obtaining their well-known extensions $\\mathbf{K}^{\\mathbf{w}}_{\\mathbf{3}}$ and $\\mathbf{PWK}$.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaa071","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T20:29:17Z","timestamp":1613161757000},"page":"186-210","source":"Crossref","is-referenced-by-count":4,"title":["On bivalent semantics and natural deduction for some infectious logics"],"prefix":"10.1093","volume":"30","author":[{"given":"Alex","family":"Belikov","sequence":"first","affiliation":[{"name":"Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University, 119234, Moscow, Russia"}]}],"member":"286","published-online":{"date-parts":[[2021,2,18]]},"reference":[{"key":"2022011721343223800_ref1","doi-asserted-by":"crossref","first-page":"113","DOI":"10.2307\/2268750","article-title":"Begr\u00fcndung einer strengen Implikation","volume":"21","author":"Ackermann","year":"1956","journal-title":"Journal of Symbolic Logic"},{"volume-title":"Entailment: The Logic of Relevance and Necessity","year":"1975","author":"Anderson","key":"2022011721343223800_ref2"},{"key":"2022011721343223800_ref3","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1093\/bjps\/IV.14.147","article-title":"Semantic information","volume":"4","author":"Bar-Hillel","year":"1953","journal-title":"British Journal for the Philosophy of Science"},{"key":"2022011721343223800_ref4","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1080\/11663081.2020.1751573","article-title":"Exactly true and non-falsity logics meeting infectious ones","volume":"30","author":"Belikov","year":"2020","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"2022011721343223800_ref5","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/978-94-010-1161-7_2","article-title":"A useful four-valued logic","volume-title":"Modern Uses of Multiple-Valued Logic","author":"Belnap","year":"1977"},{"key":"2022011721343223800_ref6","first-page":"30","article-title":"How a computer should think","volume-title":"Contemporary Aspects of Philosophy","author":"Belnap","year":"1977"},{"key":"2022011721343223800_ref7","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1080\/01445348108837023","article-title":"On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus","volume":"2","author":"Bochvar","year":"1981","journal-title":"History and Philosophy of Logic"},{"year":"2020","author":"Bonzio","article-title":"Containment logics and Plonka sums of matrices","key":"2022011721343223800_ref8"},{"key":"2022011721343223800_ref9","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s00153-020-00727-6","article-title":"Logics of left variable inclusion and Plonka sums of matrices","volume":"60","author":"Bonzio","year":"2021","journal-title":"Archive for Mathematical Logic"},{"key":"2022011721343223800_ref10","first-page":"165","article-title":"Characterizing logical consequence in paraconsistent weak Kleene","volume-title":"New Developments in Logic and the Philosophy of Science","author":"Ciuni","year":"2016"},{"key":"2022011721343223800_ref11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/11663081.2018.1547514","article-title":"Semantical analysis of weak Kleene logics","volume":"29","author":"Ciuni","year":"2019","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"2022011721343223800_ref12","doi-asserted-by":"crossref","first-page":"301","DOI":"10.26686\/ajl.v15i2.4864","article-title":"Relevant logics obeying component homogeneity","volume":"15","author":"Ciuni","year":"2018","journal-title":"Australasian Journal of Logic"},{"key":"2022011721343223800_ref13","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/978-3-662-59533-6_8","article-title":"Modeling the interaction of computer errors by four-valued contaminating logics","volume-title":"Logic, Language, Information, and Computation. WoLLIC 2019","author":"Ciuni","year":"2019"},{"key":"2022011721343223800_ref14","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1093\/logcom\/exz009","article-title":"Logics based on linear orders of contaminating values","volume":"29","author":"Ciuni","year":"2019","journal-title":"Journal of Logic and Computation"},{"key":"2022011721343223800_ref15","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/BF00216471","article-title":"A note on negation","volume":"32","author":"Daniels","year":"1990","journal-title":"Erkenntnis"},{"key":"2022011721343223800_ref16","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1093\/jigpal\/jzy057","article-title":"Theories of truth based on four-valued infectious logics","volume":"28","author":"Da Re","year":"2020","journal-title":"Logic Journal of the IGPL"},{"volume-title":"A Family of Conforming Relevant Logics","year":"1981","author":"Deutsch","key":"2022011721343223800_ref17"},{"key":"2022011721343223800_ref18","first-page":"26","article-title":"Relevant analytic entailment","volume":"2","author":"Deutsch","year":"1977","journal-title":"The Relevance Logic Newsletter"},{"key":"2022011721343223800_ref19","first-page":"67","article-title":"What is a theory of meaning? (II)","volume-title":"Truth and Meaning: Essays in Semantics","author":"Dummett","year":"1976"},{"key":"2022011721343223800_ref20","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BF00373152","article-title":"Intuitive semantics for first-degree entailments and coupled trees","volume":"29","author":"Dunn","year":"1976","journal-title":"Philosophical Studies"},{"key":"2022011721343223800_ref21","doi-asserted-by":"crossref","first-page":"1617","DOI":"10.1093\/logcom\/exu048","article-title":"Faulty Belnap computers and subsystems of FDE","volume":"26","author":"Ferguson","year":"2016","journal-title":"Journal of Logic and Computation"},{"key":"2022011721343223800_ref22","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10992-014-9321-y","article-title":"Logics of nonsense and parry systems","volume":"44","author":"Ferguson","year":"2015","journal-title":"Journal of Philosophical Logic"},{"key":"2022011721343223800_ref23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-70821-8","volume-title":"Meaning and Proscription in Formal Logic. Variations on the Propositional Logic of William T. Parry","author":"Ferguson","year":"2017"},{"key":"2022011721343223800_ref24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-05206-9_6","article-title":"Logics and falsifications","author":"Kapsner","year":"2014","journal-title":"Trends in Logic"},{"volume-title":"Introduction to Metamathematics","year":"1952","author":"Kleene","key":"2022011721343223800_ref25"},{"key":"2022011721343223800_ref26","doi-asserted-by":"crossref","first-page":"91","DOI":"10.12775\/LLP.1999.008","article-title":"Paraconsistency and analyticity","volume":"7","author":"Oller","year":"1999","journal-title":"Logic and Logical Philosophy"},{"key":"2022011721343223800_ref27","first-page":"268","article-title":"Conjunction and disjunction in infectious logics","volume-title":"Logic, Rationality, and Interaction. LORI 2017","author":"Omori"},{"key":"2022011721343223800_ref28","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1007\/s11225-019-09876-z","article-title":"Proof theory of paraconsistent weak Kleene logic","volume":"108","author":"Paoli","year":"2020","journal-title":"Studia Logica"},{"key":"2022011721343223800_ref29","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s11787-017-0169-0","article-title":"Natural deduction for Fitting\u2019s four-valued generalizations of Kleene\u2019s logics","volume":"11","author":"Petrukhin","year":"2017","journal-title":"Logica Universalis"},{"key":"2022011721343223800_ref30","first-page":"279","article-title":"Natural deduction systems for logics in the FDE family","volume-title":"New Essays in Belnap\u2013Dunn Logic","author":"Priest","year":"2020"},{"key":"2022011721343223800_ref31","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/978-94-017-0460-1_4","article-title":"Paraconsistent logic","volume-title":"Handbook of Philosophical Logic","author":"Priest","year":"2002"},{"key":"2022011721343223800_ref32","doi-asserted-by":"crossref","first-page":"2","DOI":"10.26686\/ajl.v11i1.1830","article-title":"Plurivalent logics","volume":"11","author":"Priest","year":"2014","journal-title":"The Australasian Journal of Logic"},{"key":"2022011721343223800_ref33","first-page":"24","article-title":"The logic of the catuskoti","volume":"1","author":"Priest","year":"2010","journal-title":"Comparative Philosophy"},{"key":"2022011721343223800_ref34","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF00258428","article-title":"The logic of paradox","volume":"8","author":"Priest","year":"1979","journal-title":"Journal of Philosophical Logic"},{"key":"2022011721343223800_ref35","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s11225-005-8474-7","article-title":"Dual intuitionistic logic and a variety of negations: the logic of scientific research","volume":"80","author":"Shramko","year":"2005","journal-title":"Studia Logica"},{"volume-title":"Truth and Falsehood: An Inquiry Into Generalized Logical Values","year":"2011","author":"Shramko","key":"2022011721343223800_ref36"},{"key":"2022011721343223800_ref37","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1007\/s11225-017-9747-7","article-title":"First degree entailment and its relatives","volume":"105","author":"Shramko","year":"2017","journal-title":"Studia Logica"},{"key":"2022011721343223800_ref38","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1007\/s10992-018-9494-x","article-title":"The Fmla-Fmla axiomatizations of the exactly true and non-falsity logics and some of their cousins","volume":"48","author":"Shramko","year":"2019","journal-title":"Journal of Philosophical Logic"},{"key":"2022011721343223800_ref39","first-page":"277","article-title":"An epistemic interpretation of paraconsistent weak Kleene logic","volume":"28","author":"Szmuc","year":"2019","journal-title":"Logic and Logical Philosophy"},{"key":"2022011721343223800_ref40","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1080\/11663081.2017.1290488","article-title":"Defining LFIs and LFUs in extensions of infectious logics","volume":"26","author":"Szmuc","year":"2016","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"2022011721343223800_ref41","doi-asserted-by":"crossref","first-page":"431","DOI":"10.26686\/ajl.v15i2.4867","article-title":"A note on Goddard and Routley\u2019s significance logic","volume":"15","author":"Szmuc","year":"2018","journal-title":"Australasian Journal of Logic"},{"key":"2022011721343223800_ref42","first-page":"207","article-title":"A theory of logical relevance","volume":"39","author":"Voishvillo","year":"1996","journal-title":"Logique et Analyse"},{"volume-title":"Philosophical-Methodological Aspects of Relevant Logic","year":"1988","author":"Voishvillo","key":"2022011721343223800_ref43"},{"key":"2022011721343223800_ref44","first-page":"331","article-title":"Logics of generalized classical truth values","volume-title":"Logica Yearbook 2014","author":"Zaitsev","year":"2015"},{"key":"2022011721343223800_ref45","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1007\/s11225-013-9534-z","article-title":"Bi-facial truth: a case for generalized truth values","volume":"101","author":"Zaitsev","year":"2013","journal-title":"Studia Logica"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/30\/1\/186\/42198238\/jzaa071.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/30\/1\/186\/42198238\/jzaa071.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,17]],"date-time":"2022-12-17T02:28:36Z","timestamp":1671244116000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/30\/1\/186\/6137707"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,18]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,2,18]]},"published-print":{"date-parts":[[2022,1,11]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzaa071","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"type":"print","value":"1367-0751"},{"type":"electronic","value":"1368-9894"}],"subject":[],"published-other":{"date-parts":[[2022,2]]},"published":{"date-parts":[[2021,2,18]]}}}