A Computational Interpretation of Modal Proofs

A Computational Interpretation of Modal Proofs (1994)

by Simone Martini , Andrea Masini

Venue:	Proof Theory of Modal Logics
Citations:	28 - 2 self

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Datum	Value	Source
TITLE	A Computational Interpretation of Modal Proofs	INFERENCE
AUTHOR NAME	Simone Martini	SVM HeaderParse 0.2
AUTHOR NAME	Andrea Masini	SVM HeaderParse 0.2
ABSTRACT	The usual (e.g. Prawitz's) treatment of natural deduction for modal logics involves a complicated rule for the introduction of the necessity, since the naive one does not allow normalization. We propose natural deduction systems for the positive fragments of the modal logics K, K4, KT, and S4, extending previous work by Masini on a two-dimensional generalization of Gentzen's sequents (2-sequents). The modal rules closely match the standard rules for an universal quantifier and different logics are obtained with simple conditions on the elimination rule for 2. We give an explicit term calculus corresponding to proofs in these systems and, after defining a notion of reduction on terms, we prove its confluence and strong normalization. 1. Introduction Proof theory of modal logics, though largely studied since the fifties, has always been a delicate subject, the main reason being the apparent impossibility to obtain elegant, natural systems for intensional operators (with the excellent ex...	user correction - Legacy Corrections
YEAR	1994	user correction - Legacy Corrections
VENUE	Proof Theory of Modal Logics	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	213--241	INFERENCE
CITATIONS	16 found	ParsCit 1.0