A simplified natural deduction approach to certain modal systems
type: Item
instance of: scholarly article
title: A simplified natural deduction approach to certain modal systems
zbMATH Open document ID: 0636.03007
author: Bangs L. Tapscott
published in: Notre Dame Journal of Formal Logic
publication date: 1987-01-01T00:00:00Z
review text: Natural deduction rules - in the manner of, say, Copi - are here defined for the normal modal systems T, S.4, B and S.5, through the device of attaching chains of numerical subscripts to lines in a derivation and restricting the introduction and elimination rules for the modal operators to appropriate configurations of subscripts. These subscripts thus do the work of subordinate proofs and restricted reiteration rules withint the more convenient format of Fitch-style natural deduction versions of the these systems. With the controlled manipulation of subscripts decision procedures for the systems are easily forthcoming. Moreover, Kripkean model-structures may readily be determined from terminated proof-tries, which generates an easy completeness theorem. The systems are extended to quantified modal logics.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 4035779
zbMATH Keywords: normal modal systems
zbMATH Keywords: subordinate proofs
zbMATH Keywords: restricted reiteration rules
zbMATH Keywords: natural deduction
zbMATH Keywords: quantified modal logics
reviewed by: Louis F. Goble
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093637557
OpenAlex ID: W2031056444
DOI: 10.1305/NDJFL/1093637557
description: scientific article; zbMATH DE number 4035779