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Divergence is diminished when the language does not contain equality with its standard interpretation.<\/jats:p>","DOI":"10.1017\/s175502032300014x","type":"journal-article","created":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T07:27:04Z","timestamp":1686122824000},"page":"1055-1069","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["FIRST-ORDER FRIENDLINESS"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5597-6794","authenticated-orcid":false,"given":"GUILLERMO","family":"BADIA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7435-9433","authenticated-orcid":false,"given":"DAVID","family":"MAKINSON","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,6,7]]},"reference":[{"key":"S175502032300014X_r4","doi-asserted-by":"publisher","DOI":"10.2307\/2272253"},{"volume-title":"Introduction to Metamathematics","year":"1952","author":"Kleene","key":"S175502032300014X_r11"},{"key":"S175502032300014X_r9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"S175502032300014X_r8","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/7.6.717"},{"volume-title":"Solvable Cases of the Decision Problem","year":"1954","author":"Ackermann","key":"S175502032300014X_r1"},{"key":"S175502032300014X_r12","first-page":"812","article-title":"What is a resplendent structure?","volume":"58","author":"Kossak","year":"2011","journal-title":"Notices of the American Mathematical Society"},{"key":"S175502032300014X_r13","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1969.tb00356.x"},{"key":"S175502032300014X_r14","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71100-5"},{"volume-title":"Beginning Model Theory: The Completeness Theorem and some Consequences","year":"1977","author":"Bridge","key":"S175502032300014X_r5"},{"key":"S175502032300014X_r3","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2023.2"},{"key":"S175502032300014X_r15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-8354-1_11"},{"volume-title":"A Method in Proofs of Undefinability","year":"1959","author":"de Bouv\u00e8re","key":"S175502032300014X_r7"},{"key":"S175502032300014X_r6","doi-asserted-by":"publisher","DOI":"10.2307\/2963593"},{"key":"S175502032300014X_r10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00660898"},{"key":"S175502032300014X_r2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19750210153"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S175502032300014X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,2]],"date-time":"2025-01-02T10:53:36Z","timestamp":1735815216000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S175502032300014X\/type\/journal_article"}},"issued":{"date-parts":[[2023,6,7]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["S175502032300014X"],"URL":"https:\/\/doi.org\/10.1017\/s175502032300014x","ISSN":["1755-0203","1755-0211"],"issn-type":[{"type":"print","value":"1755-0203"},{"type":"electronic","value":"1755-0211"}],"published":{"date-parts":[[2023,6,7]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. 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Another relation, designed to fix the problem in logic without equality, is introduced and discussed in connection with the issue of classical recapture.<\/jats:p>","DOI":"10.1017\/s1755020311000207","type":"journal-article","created":{"date-parts":[[2011,10,10]],"date-time":"2011-10-10T16:02:40Z","timestamp":1318262560000},"page":"479-485","source":"Crossref","is-referenced-by-count":8,"title":["REASSURANCE FOR THE LOGIC OF PARADOX"],"prefix":"10.1017","volume":"4","author":[{"given":"MARCEL","family":"CRABB\u00c9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,9,23]]},"reference":[{"key":"S1755020311000207_ref3","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199263301.001.0001"},{"key":"S1755020311000207_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370190"},{"key":"S1755020311000207_ref1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005208424356"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020311000207","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T06:39:15Z","timestamp":1556347155000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020311000207\/type\/journal_article"}},"issued":{"date-parts":[[2011,9]]},"references-count":3,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["S1755020311000207"],"URL":"https:\/\/doi.org\/10.1017\/s1755020311000207","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2011,9]]}},{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T00:02:19Z","timestamp":1648771339488},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T00:00:00Z","timestamp":1572825600000},"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":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2021,6]]},"abstract":"Abstract<\/jats:title>Numerous learning tasks can be described as the process of extrapolating patterns from observed data. One of the driving intuitions behind the theory of algorithmic randomness is that randomness amounts to the absence of any effectively detectable patterns: it is thus natural to regard randomness as antithetical to inductive learning. Osherson and Weinstein [11] draw upon the identification of randomness with unlearnability to introduce a learning-theoretic framework (in the spirit of formal learning theory) for modelling algorithmic randomness. They define two success criteria\u2014specifying under what conditions a pattern may be said to have been detected by a computable learning function\u2014and prove that the collections of data sequences on which these criteria cannot be satisfied correspond to the set of weak 1-randoms and the set of weak 2-randoms, respectively. This learning-theoretic approach affords an intuitive perspective on algorithmic randomness, and it invites the question of whether restricting attention to learning-theoretic success criteria comes at an expressivity cost. In other words, is the framework expressive enough to capture most core algorithmic randomness notions and, in particular, Martin-L\u00f6f randomness\u2014arguably, the most prominent algorithmic randomness notion in the literature? In this article, we answer the latter question in the affirmative by providing a learning-theoretic characterisation of Martin-L\u00f6f randomness. We then show that Schnorr randomness, another central algorithmic randomness notion, also admits a learning-theoretic characterisation in this setting.<\/jats:p>","DOI":"10.1017\/s175502031900042x","type":"journal-article","created":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T11:17:35Z","timestamp":1572866255000},"page":"531-549","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["A LEARNING-THEORETIC CHARACTERISATION OF MARTIN-L\u00d6F RANDOMNESS AND SCHNORR RANDOMNESS"],"prefix":"10.1017","volume":"14","author":[{"given":"FRANCESCA","family":"ZAFFORA BLANDO","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2019,11,4]]},"reference":[{"key":"S175502031900042X_r7","first-page":"337","article-title":"Uniform tests of randomness","volume":"17","author":"Levin","year":"1976","journal-title":"Soviet Mathematics 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University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2013,3,13]],"date-time":"2013-03-13T00:00:00Z","timestamp":1363132800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2013,9]]},"abstract":"Abstract<\/jats:title>Straightforwardly and strictly intuitionistic inferences show that the Brouwer\u2013 Heyting\u2013Kolmogorov (BHK) interpretation, in the presence of a formulation of the recognition principle, entails the validity of the Law of Testability: that the form \u00ac f<\/jats:italic> V \u00ac\u00ac f<\/jats:italic> is valid. Therefore, the BHK and recognition, as described here, are inconsistent with the axioms both of intuitionistic mathematics and of Markovian constructivism. This finding also implies that, if the BHK and recognition are suitably formulated, then Brouwer\u2019s original weak counterexample reasoning was fallacious. The results of the present article extend and refine those of McCarty, C. (2012). Antirealism and Constructivism: Brouwer\u2019s Weak Counterexamples<\/jats:italic>. The Review of Symbolic Logic. First View. Cambridge University Press.<\/jats:p>","DOI":"10.1017\/s1755020313000051","type":"journal-article","created":{"date-parts":[[2013,3,13]],"date-time":"2013-03-13T09:12:42Z","timestamp":1363165962000},"page":"513-523","source":"Crossref","is-referenced-by-count":0,"title":["BROUWER\u2019S WEAK COUNTEREXAMPLES AND TESTABILITY: FURTHER REMARKS"],"prefix":"10.1017","volume":"6","author":[{"given":"CHARLES","family":"MCCARTY","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2013,3,13]]},"reference":[{"key":"S1755020313000051_ref3","volume-title":"Collected Works","volume":"1","author":"Brouwer","year":"1975"},{"key":"S1755020313000051_ref4","volume-title":"Elements of Intuitionism","author":"Dummett","year":"1977"},{"key":"S1755020313000051_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079432"},{"key":"S1755020313000051_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/2269016"},{"key":"S1755020313000051_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)70854-1"},{"key":"S1755020313000051_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565663"},{"key":"S1755020313000051_ref6","unstructured":"Goodman N. D . (1968). Intuitionistic Arithmetic as a Theory of Constructions. PhD Dissertation. Palo Alto, CA: Stanford University, p. v+111."},{"key":"S1755020313000051_ref9","first-page":"198","volume-title":"Logic, Methodology, and Philosophy of Science I","author":"Kreisel","year":"1962"},{"key":"S1755020313000051_ref13","volume-title":"Constructivism in Mathematics","volume":"I","author":"Troelstra","year":"1988"},{"key":"S1755020313000051_ref2","first-page":"152","volume-title":"De Onbetrouwbaarheid der Logische Principes. Tijdschrift voor Wijsbegeerte","volume":"2","author":"Brouwer","year":"1908"},{"key":"S1755020313000051_ref5","first-page":"215","volume-title":"Truth and Other Enigmas","author":"Dummett","year":"1978"},{"key":"S1755020313000051_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01186549"},{"key":"S1755020313000051_ref10","volume-title":"Antirealism and Constructivism: Brouwer\u2019s Weak Counterexamples","author":"McCarty","year":"2012"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020313000051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T20:06:44Z","timestamp":1556050004000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020313000051\/type\/journal_article"}},"issued":{"date-parts":[[2013,3,13]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S1755020313000051"],"URL":"https:\/\/doi.org\/10.1017\/s1755020313000051","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2013,3,13]]}},{"indexed":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T00:40:02Z","timestamp":1728175202821},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2010,8,12]],"date-time":"2010-08-12T00:00:00Z","timestamp":1281571200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2010,9]]},"abstract":"We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T<\/jats:bold>, S4<\/jats:bold>, and S5<\/jats:bold>, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of \u201cnested\u201d or \u201ctree-sequent\u201d calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario.<\/jats:p>","DOI":"10.1017\/s1755020310000134","type":"journal-article","created":{"date-parts":[[2010,8,12]],"date-time":"2010-08-12T13:21:31Z","timestamp":1281619291000},"page":"351-373","source":"Crossref","is-referenced-by-count":8,"title":["POSITIVE LOGIC WITH ADJOINT MODALITIES: PROOF THEORY, SEMANTICS, AND REASONING ABOUT INFORMATION"],"prefix":"10.1017","volume":"3","author":[{"given":"MEHRNOOSH","family":"SADRZADEH","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ROY","family":"DYCKHOFF","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,8,12]]},"reference":[{"key":"S1755020310000134_ref23","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/4.2.125"},{"key":"S1755020310000134_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129598002540"},{"key":"S1755020310000134_ref21","unstructured":"Simpson A. (1993). The Proof Theory and Semantics of Intuitionistic Modal Logic. PhD Thesis, University of Edinburgh."},{"key":"S1755020310000134_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2009.07.102"},{"key":"S1755020310000134_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-008-9414-7"},{"key":"S1755020310000134_ref18","unstructured":"Sadrzadeh M. (2006). Actions and Resources in Epistemic Logic. PhD Thesis, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al."},{"key":"S1755020310000134_ref12","unstructured":"Kriener J. , Sadrzadeh M. , & Dyckhoff R. (2009). Implementation of a cut-free sequent calculus for logics with adjoint modalities. Technical report, School of Computer Science, University of St Andrews, St Andrews, Scotland."},{"key":"S1755020310000134_ref15","volume-title":"Papers on Time and Tense","author":"Prior","year":"1968"},{"key":"S1755020310000134_ref6","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/7.6.683"},{"key":"S1755020310000134_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01061239"},{"key":"S1755020310000134_ref2","doi-asserted-by":"publisher","DOI":"10.1023\/B:SYNT.0000024912.56773.5e"},{"key":"S1755020310000134_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2009.02.037"},{"key":"S1755020310000134_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-005-2267-3"},{"key":"S1755020310000134_ref4","first-page":"71","volume-title":"Australian Joint Conference on Artificial Intelligence, Volume 1502 of Lecture Notes in Computer Science","author":"Bonnette","year":"1998"},{"key":"S1755020310000134_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01053026"},{"key":"S1755020310000134_ref9","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/6.3.451"},{"key":"S1755020310000134_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.04.007"},{"key":"S1755020310000134_ref1","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exm015"},{"key":"S1755020310000134_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"S1755020310000134_ref5","first-page":"107","volume-title":"Advances in Modal Logic","volume":"6","author":"Br\u00fcnnler","year":"2006"},{"key":"S1755020310000134_ref10","volume-title":"Logic in Computer Science","author":"Huth","year":"2000"},{"key":"S1755020310000134_ref13","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/3.2-3.371"},{"key":"S1755020310000134_ref16","doi-asserted-by":"publisher","DOI":"10.4324\/9780203252642"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020310000134","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T21:42:36Z","timestamp":1556401356000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020310000134\/type\/journal_article"}},"issued":{"date-parts":[[2010,8,12]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S1755020310000134"],"URL":"https:\/\/doi.org\/10.1017\/s1755020310000134","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2010,8,12]]}},{"indexed":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T23:10:04Z","timestamp":1710371404899},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,3,1]],"date-time":"2009-03-01T00:00:00Z","timestamp":1235865600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. symb. logic"],"published-print":{"date-parts":[[2009,3]]},"abstract":"This essay proposes a procedural interpretation of negative information in terms of split negation as procedural prohibition. Information frames and models are introduced, with negation defined as the implication of bottom,0<\/jats:bold>. A method for extracting the procedures prohibited by complex formulas is outlined, and the relationship between types of prohibited procedures is identified. Definitions of negation types in terms of the implication of0<\/jats:bold>on an informational interpretation have been criticized. This criticism turns on the definitions creating a purportedly unnatural asymmetry between positive and negative information. It is demonstrated below that a strong asymmetry between positive and negative information is in fact the case. As such, an asymmetry between positive and negative information is natural, and something that we should want an informational interpretation of negation to preserve.<\/jats:p>","DOI":"10.1017\/s1755020309090133","type":"journal-article","created":{"date-parts":[[2009,5,28]],"date-time":"2009-05-28T08:30:51Z","timestamp":1243499451000},"page":"233-248","source":"Crossref","is-referenced-by-count":4,"title":["DYNAMIC NEGATION AND NEGATIVE INFORMATION"],"prefix":"10.1017","volume":"2","author":[{"given":"SEBASTIAN","family":"SEQUOIAH-GRAYSON","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,1]]},"reference":[{"key":"S1755020309090133_ref7","doi-asserted-by":"publisher","DOI":"10.1023\/B:MIND.0000021684.50925.c9"},{"key":"S1755020309090133_ref15","first-page":"409","volume-title":"The Philosophy of Information and Logic, Synthese","volume":"167","author":"Sequoiah-Grayson","year":"2009"},{"key":"S1755020309090133_ref1","first-page":"29","article-title":"Non-commutative logic, I: The multiplicative fragment","author":"Abrusci","year":"2000","journal-title":"Annals of Pure and Applied Logic"},{"key":"S1755020309090133_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"key":"S1755020309090133_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71685-9"},{"key":"S1755020309090133_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(64)50066-9"},{"key":"S1755020309090133_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02121114"},{"key":"S1755020309090133_ref2","first-page":"1","volume-title":"Substructural Logics, Studies in Logic and Computation No. 2","volume":"101","author":"Dosen","year":"1993"},{"key":"S1755020309090133_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-56734-8"},{"key":"S1755020309090133_ref3","volume-title":"Knowledge and the Flow of Information","author":"Dretske","year":"1981"},{"key":"S1755020309090133_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3179-9"},{"key":"S1755020309090133_ref4","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1093\/oso\/9780198537779.003.0004","volume-title":"Substructural Logics, Studies in Logic and Computation No. 2","author":"Dunn","year":"1993"},{"key":"S1755020309090133_ref5","first-page":"331","volume-title":"Philosophical Perspectives","volume":"7","author":"Dunn","year":"1994"},{"key":"S1755020309090133_ref6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1515\/9783110876802.3","volume-title":"Negation: A Notion in Focus","author":"Dunn","year":"1996"},{"key":"S1755020309090133_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s11023-007-9072-4"},{"key":"S1755020309090133_ref12","first-page":"343","volume-title":"The Philosophy of Information and Logic, Synthese","volume":"167","author":"Mares","year":"2009"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020309090133","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T22:51:56Z","timestamp":1710370316000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020309090133\/type\/journal_article"}},"issued":{"date-parts":[[2009,3]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,3]]}},"alternative-id":["S1755020309090133"],"URL":"https:\/\/doi.org\/10.1017\/s1755020309090133","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2009,3]]}},{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T04:01:57Z","timestamp":1781755317074,"version":"3.54.5"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2010,5,11]],"date-time":"2010-05-11T00:00:00Z","timestamp":1273536000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2010,9]]},"abstract":"Kripke\u2019s theory of truth offered a trivalent semantics for a language which, like English, contains a truth predicate and means of self-reference; but it did so by severely restricting the expressive power of the logic. In Kripke\u2019s analysis, the Liar (e.g.,This very sentence is not true<\/jats:italic>) receives the indeterminate truth value, but this fact cannot be expressed in the language; by contrast, it is straightforward to say in English thatthe Liar is something other than true<\/jats:italic>. Kripke\u2019s theory also fails to handle the Strengthened Liar, which can be expressed in English as:This very sentence is something other than true<\/jats:italic>. We develop a theory which seeks to overcome these difficulties, and is based on a detailed analysis of some of the linguistic means by which the Strengthened Liar can be expressed in English. In particular, we propose to takeliterally<\/jats:italic>the quantificational form of the negative expressionsomething other than true.<\/jats:italic>Like other quantifiers, it may have different implicit domain restrictions, which give rise to a variety of negations of different strengths (e.g.,something other than true among the values<\/jats:italic>{0, 1<\/jats:italic>}, oramong<\/jats:italic>{0, 1, 2<\/jats:italic>}, etc). This analysis naturally leads to a logic with as many truth values as there are ordinals\u2014a conclusion reached independently by Cook (2008a). We develop the theory within a generalization of the Strong Kleene Logic, augmented with negations that each have a nonmonotonic semantics. We show that fixed points can be constructed for our logic, and that it enjoys a limited form of \u2018expressive completeness\u2019. Finally, we discuss the relation between our theory and various alternatives, including one in which the wordtrue<\/jats:italic>(rather than negation) is semantically ambiguous, and gives rise to a hierarchy of truth predicates of increasing strength.<\/jats:p>","DOI":"10.1017\/s1755020310000067","type":"journal-article","created":{"date-parts":[[2010,5,11]],"date-time":"2010-05-11T09:20:34Z","timestamp":1273569634000},"page":"374-414","source":"Crossref","is-referenced-by-count":10,"title":["SUPER LIARS"],"prefix":"10.1017","volume":"3","author":[{"given":"PHILIPPE","family":"SCHLENKER","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,5,11]]},"reference":[{"key":"S1755020310000067_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/2024634"},{"key":"S1755020310000067_ref18","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1515\/9783110126969.7.651","volume-title":"Semantik: ein internationales Handbuch der zeitgen\u00f6ssischen Forschung","author":"Kratzer","year":"1991"},{"key":"S1755020310000067_ref17","volume-title":"Formal Pragmatics","author":"Kadmon","year":"2001"},{"key":"S1755020310000067_ref16","volume-title":"A Natural History of Negation","author":"Horn","year":"1989"},{"key":"S1755020310000067_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/BF00485622"},{"key":"S1755020310000067_ref6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023027808400"},{"key":"S1755020310000067_ref10","first-page":"396","article-title":"Universal metalanguages for philosophy","volume":"17","author":"Fitch","year":"1964","journal-title":"Metaphysics"},{"key":"S1755020310000067_ref14","doi-asserted-by":"publisher","DOI":"10.1023\/B:LOGI.0000019227.09236.f5"},{"key":"S1755020310000067_ref9","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199230747.001.0001"},{"key":"S1755020310000067_ref7","volume-title":"Liars and Heaps: New Essays on Paradox","author":"Field","year":"2003"},{"key":"S1755020310000067_ref5","doi-asserted-by":"publisher","DOI":"10.2307\/2274093"},{"key":"S1755020310000067_ref4","volume-title":"What Is a Truth Value, and How Many Are There?","author":"Cook","year":"2008"},{"key":"S1755020310000067_ref8","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1093\/oso\/9780199233915.003.0004","volume-title":"Revenge of the Liar","author":"Field","year":"2007"},{"key":"S1755020310000067_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-004-3758-3"},{"key":"S1755020310000067_ref11","unstructured":"Gajewski J. (2005). Neg-Raising: Polarity and Presupposition. Doctoral Dissertation, MIT: Cambridge, MA."},{"key":"S1755020310000067_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00453018"},{"key":"S1755020310000067_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-006-9035-x"},{"key":"S1755020310000067_ref13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010314719817"},{"key":"S1755020310000067_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s11050-009-9043-9"},{"key":"S1755020310000067_ref1","doi-asserted-by":"publisher","DOI":"10.2307\/2025724"},{"key":"S1755020310000067_ref3","volume-title":"Revenge of the Liar","author":"Cook","year":"2008"},{"key":"S1755020310000067_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s11168-004-0908-2"},{"key":"S1755020310000067_ref25","volume-title":"Liars and Heaps: New Essays on Paradox","author":"Yablo","year":"2003"},{"key":"S1755020310000067_ref12","unstructured":"Galinon H. (2006). Comments on Schlenker. Hand-out of a talk given at the 3rd Paris-Amsterdam Logic Meeting of Young Researchers (PALMYR 3), held at Institut Jean-Nicod, Paris on June 28, 2006."},{"key":"S1755020310000067_ref24","doi-asserted-by":"crossref","first-page":"123","DOI":"10.7551\/mitpress\/4056.003.0006","volume-title":"Ken Hale: A Life in Language","author":"von Fintel","year":"2001"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020310000067","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T17:22:16Z","timestamp":1711473736000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020310000067\/type\/journal_article"}},"issued":{"date-parts":[[2010,5,11]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S1755020310000067"],"URL":"https:\/\/doi.org\/10.1017\/s1755020310000067","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2010,5,11]]}},{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T20:45:43Z","timestamp":1783111543773,"version":"3.54.6"},"reference-count":47,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T00:00:00Z","timestamp":1570579200000},"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":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2020,12]]},"abstract":"Abstract<\/jats:title>In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge 35. Building on Stalnaker\u2019s core insights, and using frameworks developed in 11 and 3, we employtopological<\/jats:italic>tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what isknown<\/jats:italic>and (roughly speaking) what isknowable<\/jats:italic>; we argue that the foundational axioms of Stalnaker\u2019s system rely intuitively onboth<\/jats:italic>of these notions. More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an \u201cevidence-in-hand\u201d conception of knowledge and a weaker \u201cevidence-out-there\u201d notion of whatcould come to be known<\/jats:italic>. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms ofknowledge and knowability<\/jats:italic>. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker\u2019s postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics.<\/jats:p>","DOI":"10.1017\/s1755020319000509","type":"journal-article","created":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T08:18:59Z","timestamp":1570609139000},"page":"748-775","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":8,"title":["LOGIC AND TOPOLOGY FOR KNOWLEDGE, KNOWABILITY, AND 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This general strategy was developed in the first part of our investigation. Applying the strategy to Kripke-Feferman leads to the theory Modal Kripke-Feferman which we discuss from the three perspectives that we had already considered in the first paper, where we discussed the theory Modal Friedman-Sheard. That is, we first show that Modal Kripke-Feferman preserves theoremhood modulo translation with respect to modal operator logic. Second, we develop a modal semantics fitting the newly developed theory. Third, we investigate whether the modal predicate of Modal Kripke-Feferman can be understood along the lines of a proposal of Kripke, namely as a truth predicate modified by a modal operator.<\/jats:p>","DOI":"10.1017\/s1755020314000069","type":"journal-article","created":{"date-parts":[[2014,4,1]],"date-time":"2014-04-01T08:40:50Z","timestamp":1396341650000},"page":"299-318","source":"Crossref","is-referenced-by-count":7,"title":["MODALITY AND AXIOMATIC THEORIES OF TRUTH II: KRIPKE-FEFERMAN"],"prefix":"10.1017","volume":"7","author":[{"given":"JOHANNES","family":"STERN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,4,1]]},"reference":[{"key":"S1755020314000069_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00305492"},{"key":"S1755020314000069_ref8","first-page":"227","volume-title":"Mathematical Logic and Formal 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University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T00:00:00Z","timestamp":1528416000000},"content-version":"unspecified","delay-in-days":7,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2018,6]]},"abstract":"Abstract<\/jats:title>The connection between the rules and derivations of Gentzen\u2019s calculiNJ<\/jats:italic><\/jats:bold>andLJ<\/jats:italic><\/jats:bold>will be explained by several steps (i.e., systems), and an analysis of the well-known problems of the connection between reduction steps of normalization and cut elimination, from Zucker (1974) and Urban (2014), will be given.<\/jats:p>","DOI":"10.1017\/s1755020318000102","type":"journal-article","created":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T05:33:05Z","timestamp":1528435985000},"page":"347-370","source":"Crossref","is-referenced-by-count":4,"title":["AN ANALYSIS OF THE RULES OF GENTZEN\u2019SNJ<\/i><\/b>ANDLJ<\/i><\/b>"],"prefix":"10.1017","volume":"11","author":[{"given":"MIRJANA","family":"BORISAVLJEVI\u0106","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2018,6,8]]},"reference":[{"key":"S1755020318000102_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/2274279"},{"key":"S1755020318000102_ref5","first-page":"176","volume-title":"The Collected Papers of Gerhard 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(1997). Sequents, Natural Deduction and Multicategories (in Serbian). Ph.D. Thesis, University of Belgrade."},{"key":"S1755020318000102_ref12","doi-asserted-by":"publisher","DOI":"10.2178\/bsl\/1208442829"},{"key":"S1755020318000102_ref20","first-page":"1","article-title":"The correspondence between cut-elimination and normalization","volume":"7","author":"Zucker","year":"1974","journal-title":"Annals of Pure and Applied Logic"},{"key":"S1755020318000102_ref14","first-page":"323","article-title":"Normalization as a homomorphic image of cut elimination","volume":"12","author":"Pottinger","year":"1977","journal-title":"Annals of Pure and Applied Logic"},{"key":"S1755020318000102_ref2","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/14.6.769"},{"key":"S1755020318000102_ref7","doi-asserted-by":"publisher","DOI":"10.2307\/2025206"},{"key":"S1755020318000102_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511527340"},{"key":"S1755020318000102_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s001530100091"},{"key":"S1755020318000102_ref11","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310047"},{"key":"S1755020318000102_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-7548-0_2"},{"key":"S1755020318000102_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139168717"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020318000102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T02:45:10Z","timestamp":1693709110000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020318000102\/type\/journal_article"}},"issued":{"date-parts":[[2018,6]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["S1755020318000102"],"URL":"https:\/\/doi.org\/10.1017\/s1755020318000102","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2018,6]]}},{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T12:36:46Z","timestamp":1772368606833,"version":"3.50.1"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T00:00:00Z","timestamp":1546992000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2019,6]]},"abstract":"Abstract<\/jats:title>Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.<\/jats:p>","DOI":"10.1017\/s1755020318000497","type":"journal-article","created":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T09:14:19Z","timestamp":1547025259000},"page":"255-270","source":"Crossref","is-referenced-by-count":11,"title":["EVERYONE KNOWS THAT SOMEONE KNOWS: QUANTIFIERS OVER EPISTEMIC AGENTS"],"prefix":"10.1017","volume":"12","author":[{"given":"PAVEL","family":"NAUMOV","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIA","family":"TAO","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2019,1,9]]},"reference":[{"key":"S1755020318000497_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/2269159"},{"key":"S1755020318000497_ref4","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093956082"},{"key":"S1755020318000497_ref5","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/5803.001.0001","volume-title":"Reasoning About Knowledge","author":"Fagin","year":"1995"},{"key":"S1755020318000497_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020308090060"},{"key":"S1755020318000497_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.04.009"},{"key":"S1755020318000497_ref9","doi-asserted-by":"publisher","DOI":"10.2307\/2964568"},{"key":"S1755020318000497_ref3","first-page":"1633","volume-title":"Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems","author":"Charrier","year":"2014"},{"key":"S1755020318000497_ref6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1970.tb00432.x"},{"key":"S1755020318000497_ref7","doi-asserted-by":"publisher","DOI":"10.1080\/11663081.1999.10510970"},{"key":"S1755020318000497_ref10","volume-title":"Symbolic Logic","author":"Lewis","year":"1932"},{"key":"S1755020318000497_ref11","volume-title":"Introduction to Mathematical Logic","author":"Mendelson","year":"2009"},{"key":"S1755020318000497_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/2268488"},{"key":"S1755020318000497_ref13","first-page":"110","volume-title":"Studies in Logic and the Foundations of Mathematics","volume":"82","author":"Sahlqvist","year":"1975"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020318000497","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,13]],"date-time":"2024-07-13T22:27:33Z","timestamp":1720909653000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020318000497\/type\/journal_article"}},"issued":{"date-parts":[[2019,1,9]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["S1755020318000497"],"URL":"https:\/\/doi.org\/10.1017\/s1755020318000497","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2019,1,9]]}},{"indexed":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T04:26:08Z","timestamp":1769401568877,"version":"3.49.0"},"reference-count":151,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T00:00:00Z","timestamp":1641168000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,9]]},"abstract":"Abstract<\/jats:title>The use of the symbol$\\mathbin {\\boldsymbol {\\vee }}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol$\\mathbin {\\boldsymbol {\\vee }}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for \u201cor,\u201dvel<\/jats:italic>. We show that the origin of the symbol$\\mathbin {\\boldsymbol {\\vee }}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>for disjunction can be traced to Whitehead and Russell\u2019s pre-Principia<\/jats:italic>work in formal logic. Because ofPrincipia<\/jats:italic>\u2019s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert\u2019s adoption of$\\mathbin {\\boldsymbol {\\vee }}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>in hisGrundz\u00fcge der theoretischen Logik<\/jats:italic>guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed.<\/jats:p>","DOI":"10.1017\/s1755020321000587","type":"journal-article","created":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T07:31:12Z","timestamp":1641195072000},"page":"862-899","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["THE GENEALOGY OF \u2018\u2019"],"prefix":"10.1017","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0513-2937","authenticated-orcid":false,"given":"LANDON D. 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In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.<\/jats:p>","DOI":"10.1017\/s175502031100030x","type":"journal-article","created":{"date-parts":[[2012,7,18]],"date-time":"2012-07-18T09:50:46Z","timestamp":1342605046000},"page":"642-664","source":"Crossref","is-referenced-by-count":12,"title":["REVISION REVISITED"],"prefix":"10.1017","volume":"5","author":[{"given":"LEON","family":"HORSTEN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GRAHAM E.","family":"LEIGH","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HANNES","family":"LEITGEB","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PHILIP","family":"WELCH","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,7,18]]},"reference":[{"key":"S175502031100030X_ref5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023027808400"},{"key":"S175502031100030X_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020308080118"},{"key":"S175502031100030X_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90073-X"},{"key":"S175502031100030X_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71123-6"},{"key":"S175502031100030X_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00649483"},{"key":"S175502031100030X_ref17","first-page":"335","volume-title":"Logic Colloquium \u201978","author":"Schmerl","year":"1979"},{"key":"S175502031100030X_ref3","doi-asserted-by":"publisher","DOI":"10.2307\/2274902"},{"key":"S175502031100030X_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/2274021"},{"key":"S175502031100030X_ref11","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1093\/oso\/9780199287116.003.0013","volume-title":"Deflationism and Paradox","author":"Halbach","year":"2005"},{"key":"S175502031100030X_ref15","volume-title":"Recent Essays on Truth and the Liar Paradox","author":"Martin","year":"1984"},{"key":"S175502031100030X_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511921049"},{"key":"S175502031100030X_ref12","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1146620166"},{"key":"S175502031100030X_ref9","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1305\/ndjfl\/1040511340","article-title":"A system of complete and consistent truth","volume":"35","author":"Halbach","year":"1994","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S175502031100030X_ref13","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9780262015868.001.0001"},{"key":"S175502031100030X_ref21","doi-asserted-by":"publisher","DOI":"10.2307\/2687753"},{"key":"S175502031100030X_ref8","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/5938.001.0001","volume-title":"The Revision Theory of Truth","author":"Gupta","year":"1993"},{"key":"S175502031100030X_ref14","first-page":"53","volume-title":"Outline of a Theory of Truth","author":"Kripke","year":"1975"},{"key":"S175502031100030X_ref20","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635425"},{"key":"S175502031100030X_ref6","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199230747.001.0001"},{"key":"S175502031100030X_ref1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199233915.001.0001","volume-title":"Revenge of the Liar. 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These results show that if two or more agents, who have epistemic and credal states that are defined over algebras that do not include any self-locating propositions, have certain information about one another\u2019s epistemic and credal states, then such agents must assign the same credence to certain propositions. I show, however, that both of these theorems fail when we consider agents who have epistemic and credal states that are defined over algebras that do include self-locating propositions. Importantly, these theorems fail for such agents even when we restrict our attention to the credences that such agents have in non-self-locating propositions. Having established this negative result, I then outline and prove three agreement theorems that hold for such agents.<\/jats:p>","DOI":"10.1017\/s1755020316000101","type":"journal-article","created":{"date-parts":[[2016,4,5]],"date-time":"2016-04-05T06:29:39Z","timestamp":1459837779000},"page":"380-407","source":"Crossref","is-referenced-by-count":2,"title":["AGREEMENT THEOREMS FOR SELF-LOCATING BELIEF"],"prefix":"10.1017","volume":"9","author":[{"given":"MICHAEL","family":"CAIE","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,4,5]]},"reference":[{"key":"S1755020316000101_ref7","unstructured":"Caie Michael . (2016). Agreement and updating for self-locating belief. (ms)."},{"key":"S1755020316000101_ref15","doi-asserted-by":"publisher","DOI":"10.2307\/2184843"},{"key":"S1755020316000101_ref16","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/61.3.171"},{"key":"S1755020316000101_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(85)90035-3"},{"key":"S1755020316000101_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s11098-006-9036-1"},{"key":"S1755020316000101_ref5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005551304409"},{"key":"S1755020316000101_ref13","doi-asserted-by":"publisher","DOI":"10.1080\/00201749708602461"},{"key":"S1755020316000101_ref4","first-page":"365","volume-title":"Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning about Knowledge","author":"Barwise","year":"1988"},{"key":"S1755020316000101_ref14","volume-title":"Convention","author":"Lewis","year":"1969"},{"key":"S1755020316000101_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343654"},{"key":"S1755020316000101_ref6","volume-title":"Anthropic Bias","author":"Bostrom","year":"2002"},{"key":"S1755020316000101_ref1","doi-asserted-by":"publisher","DOI":"10.5840\/jphil2003100729"},{"key":"S1755020316000101_ref10","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/60.2.143"},{"key":"S1755020316000101_ref12","first-page":"11","article-title":"People with common priors can agree to disagree","volume":"8","author":"Lederman","year":"2015","journal-title":"this Review"},{"key":"S1755020316000101_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-013-0280-6"},{"key":"S1755020316000101_ref17","doi-asserted-by":"publisher","DOI":"10.1080\/713659799"},{"key":"S1755020316000101_ref11","volume-title":"Reasoning About Knowledge","author":"Halpern","year":"1995"},{"key":"S1755020316000101_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-012-9236-4"},{"key":"S1755020316000101_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(90)90057-Q"}],"container-title":["The Review of Symbolic Logic"],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020316000101","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T23:36:40Z","timestamp":1555630600000},"score":0.0,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020316000101\/type\/journal_article"}},"issued":{"date-parts":[[2016,4,5]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["S1755020316000101"],"URL":"https:\/\/doi.org\/10.1017\/s1755020316000101","ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"published":{"date-parts":[[2016,4,5]]}},{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T15:45:34Z","timestamp":1771947934399,"version":"3.50.1"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2017,6,5]],"date-time":"2017-06-05T00:00:00Z","timestamp":1496620800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2017,12]]},"abstract":"Abstract<\/jats:title>In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo\u2013Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti\u2019s model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti\u2019s model and leads to a much more flexible approach to quantum set theory.<\/jats:p>","DOI":"10.1017\/s1755020317000120","type":"journal-article","created":{"date-parts":[[2017,6,5]],"date-time":"2017-06-05T05:46:10Z","timestamp":1496641570000},"page":"782-807","source":"Crossref","is-referenced-by-count":10,"title":["ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY"],"prefix":"10.1017","volume":"10","author":[{"given":"MASANAO","family":"OZAWA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,6,5]]},"reference":[{"key":"S1755020317000120_ref24","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1515\/dema-1985-0116","article-title":"Commutators in orthomodular lattices","volume":"18","author":"Pulmannov\u00e1","year":"1985","journal-title":"Demonstratio 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He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. In this paper, such models are used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. 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