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A łukasiewicz-style refutation system for the modal logic S

Journal of Philosophical Logic 24 (6):573 - 582 (1995)

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Rejection in Łukasiewicz's and Słupecki's Sense.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Cham, Switzerland: Springer- Birkhauser,. pp. 575-597.details The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...) Aristotelian Logic in Logic and Philosophy of Logic History of Logic, Misc in Logic and Philosophy of Logic Logical Consequence and Entailment in Logic and Philosophy of Logic Mathematical Logic in Philosophy of Mathematics Mathematical Methodology in Philosophy of Mathematics $75.58 used $86.51 new (collection) View on Amazon.com Direct download (3 more) Export citation Bookmark 2 citations
On Pairs of Dual Consequence Operations.Urszula Wybraniec-Skardowska & Jacek Waldmajer - 2011 - Logica Universalis 5 (2):177-203.details In the paper, the authors discuss two kinds of consequence operations characterized axiomatically. The first one are consequence operations of the type Cn + that, in the intuitive sense, are infallible operations, always leading from accepted (true) sentences of a deductive system to accepted (true) sentences of the deductive system (see Tarski in Monatshefte für Mathematik und Physik 37:361–404, 1930, Comptes Rendus des Séances De la Société des Sciences et des Lettres de Varsovie 23:22–29, 1930; Pogorzelski and Słupecki in Stud (...) Logic and Philosophy of Logic Logical Consequence and Entailment in Logic and Philosophy of Logic Nonclassical Logics in Logic and Philosophy of Logic $47.60 new $52.55 used $54.99 from Amazon (collection) View on Amazon.com Direct download (5 more) Export citation Bookmark 7 citations
Syntactic Refutations against Finite Models in Modal Logic.Tomasz Skura - 1994 - Notre Dame Journal of Formal Logic 35 (4):595-605.details The purpose of the paper is to study syntactic refutation systems as a way of characterizing normal modal propositional logics. In particular it is shown that there is a decidable modal logic without the finite model property that has a simple finite refutation system. Modal Logic in Logic and Philosophy of Logic Modal and Intensional Logic in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark 5 citations
Refutation-Aware Gentzen-Style Calculi for Propositional Until-Free Linear-Time Temporal Logic.Norihiro Kamide - 2023 - Studia Logica 111 (6):979-1014.details This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson’s paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven. Proof Theory in Logic and Philosophy of Logic Temporal Logic in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 1 citation
Falsification-Aware Calculi and Semantics for Normal Modal Logics Including S4 and S5.Norihiro Kamide - 2023 - Journal of Logic, Language and Information 32 (3):395-440.details Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson’s constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved. Modal and Intensional Logic in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 1 citation
Which Modal Logic Is the Right One?John P. Burgess - 1999 - Notre Dame Journal of Formal Logic 40 (1):81-93.details The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, (...) Modal and Intensional Logic in Logic and Philosophy of Logic Direct download (6 more) Export citation Bookmark 36 citations
Proof and truth: an anti-realist perspective.Luca Tranchini - 2013 - Pisa: Edizioni ETS. Edited by Luca Tranchini.details In the first chapter, we discuss Dummetts idea that the notion of truth arises from the one of the correctness of an assertion. We argue that, in a first-order language, the need of defining truth in terms of the notion of satisfaction, which is yielded by the presence of quantifiers, is structurally analogous to the need of a notion of truth as distinct from the one of correctness of an assertion. In the light of the analogy between predicates in Frege (...) Semantic Anti-Realism in Metaphysics Truth in Philosophy of Language Direct download Export citation Bookmark 4 citations
Rejection in Łukasiewicz's and Słupecki' Sense.Urszula Wybraniec-Skardowska - 2018 - Lvov-Warsaw School. Past and Present.details The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...) Aristotelian Logic in Logic and Philosophy of Logic Brentano School in 19th Century Philosophy History of Logic, Misc in Logic and Philosophy of Logic Logical Consequence and Entailment in Logic and Philosophy of Logic Logics, Misc in Logic and Philosophy of Logic Proof Theory in Logic and Philosophy of Logic Direct download Export citation Bookmark
A note on relationship between the consequence operations cn and dcn.Anna Gomolinska & Justyna K. Myslinska - 2000 - Bulletin of the Section of Logic 29 (1/2):63-67.details Logics in Logic and Philosophy of Logic Nonclassical Logics in Logic and Philosophy of Logic Direct download Export citation Bookmark

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