This paper studies proof systems for the logics of super-strict implication ST2–ST5, which correspond to C.I. Lewis’ systems S2–S5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating STn in Sn and backsimulating Sn in STn, respectively (for n = 2, ..., 5). Next, G3-style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of G3-style calculi, that they are sound and complete, and it is shown that the proof search for G3.ST2 is terminating and therefore the logic is decidable.

Proof systems for super-strict implication

guido gherardi
Co-primo
Writing – Original Draft Preparation
;
eugenio orlandelli
Co-primo
Writing – Original Draft Preparation
;
2023

Abstract

This paper studies proof systems for the logics of super-strict implication ST2–ST5, which correspond to C.I. Lewis’ systems S2–S5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating STn in Sn and backsimulating Sn in STn, respectively (for n = 2, ..., 5). Next, G3-style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of G3-style calculi, that they are sound and complete, and it is shown that the proof search for G3.ST2 is terminating and therefore the logic is decidable.
2023
guido gherardi, eugenio orlandelli, eric raidl
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/926906
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