n this paper we study the proof theory of C.I. Lewis’ logics of strict conditional S1- S5 and we propose the first modular and uniform presentation of C.I. Lewis’ systems. In particular, for each logic Sn we present a labelled sequent calculus G3Sn and we discuss its structural properties: every rule is height-preserving invertible and the structural rules of weakening, contraction and cut are admissible. Completeness of G3Sn is established both indirectly via the embedding in the axiomatic system Sn and directly via the extraction of a countermodel out of a failed proof search. Finally, the sequent calculus G3S1 is employed to obtain a syntactic proof of decidability of S1.

Labelled sequent calculi for logics of strict implication

Tesi, Matteo
2022

Abstract

n this paper we study the proof theory of C.I. Lewis’ logics of strict conditional S1- S5 and we propose the first modular and uniform presentation of C.I. Lewis’ systems. In particular, for each logic Sn we present a labelled sequent calculus G3Sn and we discuss its structural properties: every rule is height-preserving invertible and the structural rules of weakening, contraction and cut are admissible. Completeness of G3Sn is established both indirectly via the embedding in the axiomatic system Sn and directly via the extraction of a countermodel out of a failed proof search. Finally, the sequent calculus G3S1 is employed to obtain a syntactic proof of decidability of S1.
2022
Settore M-FIL/02 - Logica e Filosofia della Scienza
14th Conference on Advances in Modal Logic, AiML 2022
fra
2022
Advances in Modal Logic. Volume 14
College publications
9781848904132
Strict implication; non-normal modalities; S1; sequent calculi cut elimination
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/131385
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