Ground and free-variable tableaux for variants of quantified modal logics

Studia Logica 69 (1):97-131 (2001)
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Abstract

In this paper we study proof procedures for some variants of first-order modal logics, where domains may be either cumulative or freely varying and terms may be either rigid or non-rigid, local or non-local. We define both ground and free variable tableau methods, parametric with respect to the variants of the considered logics. The treatment of each variant is equally simple and is based on the annotation of functional symbols by natural numbers, conveying some semantical information on the worlds where they are meant to be interpreted.This paper is an extended version of a previous work where full proofs were not included. Proofs are in some points rather tricky and may help in understanding the reasons for some details in basic definitions.

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References found in this work

Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Display logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.
Indexed systems of sequents and cut-elimination.Grigori Mints - 1997 - Journal of Philosophical Logic 26 (6):671-696.
Predicate logics on display.Heinrich Wansing - 1999 - Studia Logica 62 (1):49-75.

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