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Intermediate logics preserving admissible inference rules of heyting calculus
Author(s) -
Rybakov Vladimir V.
Publication year - 1993
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19930390144
Subject(s) - t norm fuzzy logics , mathematics , propositional calculus , rule of inference , property (philosophy) , inference , intermediate logic , intuitionistic logic , monoidal t norm logic , classical logic , propositional variable , calculus (dental) , proof calculus , well formed formula , discrete mathematics , algebra over a field , natural deduction , pure mathematics , description logic , computer science , theoretical computer science , artificial intelligence , epistemology , philosophy , dentistry , fuzzy logic , membership function , fuzzy set , fuzzy number , medicine
The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which describe all tabular logics preserving admissibility: a tabular logic λ preserves all admissible rules for H iff 7λ has width not more than 2 and is not included in each λ. MSC: 03B55, 03B20.