The Finite Model Property for the Implicational Fragment of IPC Without Exchange and Contraction

Authors: van Alten, C.¹; Raftery, J.²

Source: Studia Logica, Volume 63, Number 2, September 1999 , pp. 213-222(10)

Publisher: Springer

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Abstract:

The aim of this paper is to show that the implicational fragment BKof the intuitionistic propositional calculus (IPC) without the rules of exchange and contraction has the finite model property with respect to the quasivariety of left residuation algebras (its equivalent algebraic semantics). It follows that the variety generated by all left residuation algebras is generated by the finite left residuation algebras. We also establish that BKhas the finite model property with respect to a class of structures that constitute a Kripke-style relational semantics for it. The results settle a question of Ono and Komori [OK85].

Keywords: substructural logic; algebraization; residuation algebra; Kripke semantics

Document Type: Research article

DOI: http://dx.doi.org/10.1023/A:1005262630549

Affiliations: 1: Email: cjvanalten@yahoo.com rafter@scifs1.und.ac.za 2: Email: cjvanalten@yahoo.com

Publication date: 1999-09-01