All Finitely Axiomatizable Normal Extensions of K4.3 are Decidable

✍ Scribed by Michael Zakharyaschevm; Alexander Alekseev

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 546 KB
• Volume: 41
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19950410103

✦ Synopsis

We use the apparatus of the canonical formulas introduced by Zakharyaschev [lo] 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.