Studia Logica 102 (3):577-607 (2014)

Authors
Gillman Payette
University of British Columbia
Abstract
This paper presents proofs of completeness and decidability of a non-temporal fragment of an Xstit logic. This shows a distinction between the non-temporal fragments of Xstit logic and regular stit logic since the latter is undecidable. The proof of decidability is via the finite model property. The finite model property is shown to hold by constructing a filtration. However, the set that is used to filter the models isn’t simply closed under subformulas, it has more complex closure conditions. The filtration set is akin to the Fischer–Ladner closure of a set used to show completeness and decidability of propositional dynamic logic
Keywords Stit  Xstit  Decidability  Kripke models
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DOI 10.1007/s11225-013-9492-5
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Agency and Deontic Logic.John F. Horty - 2001 - Oxford, England: Oxford University Press.
Normal Forms in Modal Logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.

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