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Syntactic Refutations against Finite Models in Modal Logic

Notre Dame Journal of Formal Logic 35 (4):595-605 (1994)

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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
A Generalisation of a Refutation-related Method in Paraconsistent Logics.Adam Trybus - forthcoming - Logic and Logical Philosophy.details Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 1 citation
A refutation theory.Tomasz Skura - 2009 - Logica Universalis 3 (2):293-302.details A general theory of refutation systems is given. Some applications (concerning maximality and minimality in lattices of logics) are also discussed. Logic and Philosophy of Logic Polish Philosophy in European Philosophy $47.60 new $52.55 used $54.99 from Amazon (collection) View on Amazon.com Direct download (3 more) Export citation Bookmark 10 citations
Admissibility and refutation: some characterisations of intermediate logics.Jeroen P. Goudsmit - 2014 - Archive for Mathematical Logic 53 (7-8):779-808.details Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics (...) Nonclassical Logics in Logic and Philosophy of Logic Direct download (4 more) Export citation Bookmark 3 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

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