Falsification-Aware Calculi and Semantics for Normal Modal Logics Including S4 and S5

Journal of Logic, Language and Information 32 (3):395-440 (2023)
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Abstract

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.

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10.1007/s10849-022-09386-7

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Citations of this work

Symmetric and conflated intuitionistic logics.Norihiro Kamide - forthcoming - Logic Journal of the IGPL.

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References found in this work

Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Aristotle's Syllogistic from the Standpoint of Modern Formal Logic.JAN LUKASIEWICZ - 1951 - Revue de Métaphysique et de Morale 57 (4):456-458.
Intuitionistic logic with strong negation.Yuri Gurevich - 1977 - Studia Logica 36 (1-2):49 - 59.

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