Proving unprovability in some normal modal logics

Bulletin of the Section of Logic 20 (1):23-29 (1991)
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Abstract

This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula  either `  or a  (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.

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Valentin Goranko
Stockholm University

Citations of this work

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.
A łukasiewicz-style refutation system for the modal logic S.Tomasz Skura - 1995 - Journal of Philosophical Logic 24 (6):573 - 582.

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References found in this work

An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
Aristotle's Syllogistic from the Standpoint of Modern Formal Logic.JAN LUKASIEWICZ - 1951 - Revue de Métaphysique et de Morale 57 (4):456-458.
Modal Logic and Classical Logic.R. A. Bull - 1987 - Journal of Symbolic Logic 52 (2):557-558.

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