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Refutation systems in modal logic

Studia Logica 53 (2):299 - 324 (1994)

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  1. The Method of Axiomatic Rejection for the Intuitionistic Propositional Logic.Rafal Dutkiewicz - 1989 - Studia Logica 48 (4):449-459.
    We prove that the intuitionistic sentential calculus is Ł-decidable, i.e. the sets of these of Int and of rejected formulas are disjoint and their union is equal to all formulas. A formula is rejected iff it is a sentential variable or is obtained from other formulas by means of three rejection rules. One of the rules is original, the remaining two are Łukasiewicz's rejection rules: by detachement and by substitution. We extensively use the method of Beth's semantic tableaux.
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  • Proof of Ł-Decidability of Lewis System S5.Jerzy Słupecki & Grzegorz Bryll - 1973 - Studia Logica 32 (1):99-105.
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  • Eine Unableitbarkeitsbeweismethode für den intuitionistischen Aussagenkalkul.G. Kreisel - 1957 - Archive for Mathematical Logic 3 (3/4):74.
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  • Proof of Ł-Decidability of Lewis System S.Jerzy Słupecki & Grzegorz Bryll - 1973 - Studia Logica 32 (1):99 - 107.
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  • On Proofs of Rejection.Walenty Staszek - 1971 - Studia Logica 29 (1):17 - 25.
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  • Theory of Rejected Propositions. I.Jerzy Słupecki, Grzegorz Bryll & Urszula Wybraniec-Skardowska - 1971 - Studia Logica 29 (1):75 - 123.
    The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of papers (...)
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  • On Decision Procedures for Sentential Logics.Tomasz Skura - 1991 - Studia Logica 50 (2):173 - 179.
    In Section 2 I give a criterion of decidability that can be applied to logics (i.e. Tarski consequence operators) without the finite model property. In Section 3 I study ukasiewicz-style refutation procedures as a method of obtaining decidability results.This method also proves to be more general than Harrop's criterion.
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  • Aristotle's Syllogistic from the Standpoint of Modern Formal Logic.JAN LUKASIEWICZ - 1952 - Revue de Métaphysique et de Morale 57 (4):456-458.
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  • Aristotle's Syllogistic From the Standpoint of Modern Formal Logic.JAN LUKASIEWICZ - 1951 - Garland.
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  • A Companion to Modal Logic.G. E. Hughes & M. J. Cresswell - 1995 - Studia Logica 54 (3):411-413.
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  • An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
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  • On Pure Refutation Formulations of Sentential Logics.Tomasz Skura - 1990 - Bulletin of the Section of Logic 19 (3):102-107.
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