An Observation Concerning Porte’s Rule in Modal Logic

Author:

French Rohan,Humberstone Lloyd

Abstract

It is well known that no consistent normal modal logic contains (as theorems) both ◊A and ◊¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ◊A, or else no consistent normal modal logic contains ◊¬A.

Publisher

Uniwersytet Lodzki (University of Lodz)

Subject

Logic,Philosophy

Reference15 articles.

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4. Fagin R., Halpern J. Y., and Vardi M. Y., What is an Inference Rule?, Journal of Symbolic Logic 57 (1992), pp. 1018–1045.

5. French Rohan, Denumerably Many Post-complete Normal Modal Logics with Propositional Constants, Notre Dame Journal of Formal Logic 53 (2012), pp. 549–556.

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1. About the Unification Types of Modal Logics;Outstanding Contributions to Logic;2024

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