Defining relevant implication in a propositionally quantified S

Journal of Symbolic Logic 62 (4):1057-1069 (1997)
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Abstract

R. K. Meyer once gave precise form to the question of whether relevant implication can be defined in any modal system, and his answer was `no'. In the present paper, we extend S4, first with propositional quantifiers, to the system S4π+; and then with definite propositional descriptions, to the system S4π+ lp . We show that relevant implication can in some sense be defined in the modal system S4π+ lp , although it cannot be defined in S4π+

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10.2307/2275626

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Philip Kremer
University of Toronto at Scarborough

Citations of this work

Logical consequence as truth-preservation.Stephen Read - 2003 - Logique and Analyse 183 (4):479-493.
A modal perspective on monadic second-order alternation hierarchies.Antti Kuusisto - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 231-247.

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References found in this work

On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.
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.
Symbolic Logic.C. I. Lewis & C. H. Langford - 1932 - Erkenntnis 4 (1):65-66.
Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.

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