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Minimal Axiomatization in Modal Logic
Author(s) -
Bellissima Fabio,
Cittadini Saverio
Publication year - 1997
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.19970430112
Subject(s) - mathematics , modal logic , transitive relation , characterization (materials science) , frame (networking) , normal modal logic , modal , discrete mathematics , intermediate logic , s5 , pure mathematics , algebra over a field , combinatorics , computer science , theoretical computer science , description logic , chemistry , polymer chemistry , telecommunications , materials science , nanotechnology
We consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K.