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An Infinitary Graded Modal Logic (Graded Modalities VI)
Author(s) -
FattorosiBarnaba Maurizio,
Grassotti Silvano
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.19950410410
Subject(s) - mathematics , countable set , modal logic , predicate logic , completeness (order theory) , predicate (mathematical logic) , modal , discrete mathematics , dynamic logic (digital electronics) , extension (predicate logic) , modalities , predicate variable , calculus (dental) , pure mathematics , multimodal logic , algebra over a field , zeroth order logic , computer science , artificial intelligence , mathematical analysis , description logic , programming language , medicine , social science , dentistry , transistor , voltage , chemistry , sociology , quantum mechanics , physics , polymer chemistry
We prove a completeness theorem for K ω1 0 , the infinitary extension of the graded version K 0 of the minimal normal logic K, allowing conjunctions and disjunctions of countable sets of formulas. This goal is achieved using both the usual tools of the normal logics with graded modalities and the machinery of the predicate infinitary logics in a version adapted to modal logic.