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All Finitely Axiomatizable Normal Extensions of K4.3 are Decidable
Author(s) -
Zakharyaschevm Michael,
Alekseev Alexander
Publication year - 1995
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.19950410103
Subject(s) - decidability , mathematics , axiom , class (philosophy) , frame (networking) , argument (complex analysis) , discrete mathematics , modal logic , pure mathematics , modal , algebra over a field , computer science , geometry , telecommunications , biochemistry , chemistry , artificial intelligence , polymer chemistry
We use the apparatus of the canonical formulas introduced by Zakharyaschev [10] to prove that all finitely axiomatizable normal modal logics containing K4.3 are decidable, though possibly not characterized by classes of finite frames. Our method is purely frame‐theoretic. Roughly, given a normal logic L above K4.3, we enumerate effectively a class of (possibly infinite) frames with respect to which L is complete, show how to check effectively whether a frame in the class validates a given formula, and then apply a Harropstyle argument to establish the decidability of L , provided of course that it has finitely many axioms.