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The Modality of Finite (Graded Modalities VII)
Author(s) -
FattorosiBarnaba Maurizio,
Balestrini Uliano Paolozzi
Publication year - 1999
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.19990450406
Subject(s) - modality (human–computer interaction) , axiom , mathematics , completeness (order theory) , modal operator , modalities , operator (biology) , extension (predicate logic) , consistency (knowledge bases) , modal , calculus (dental) , algebra over a field , discrete mathematics , pure mathematics , modal logic , mathematical analysis , computer science , artificial intelligence , geometry , programming language , medicine , social science , dentistry , repressor , chemistry , sociology , biochemistry , transcription factor , polymer chemistry , gene
We prove a completeness theorem for K f , an extension of K by the operator ⋄ f that means “there exists a finite number of accessible worlds such that … is true, plus suitable axioms to rule it. This is done by an application of the method of consistency properties for modal systems as in [4] with suitable adaptations. Despite no graded modality is invoked here, we consider this work as pertaining to that area both because ⋄ f is a definable operator in the graded infinitary system K ω1 0 (see [4]), and because this idea was the original source for the development of graded modalities.