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  1. Logical Consecutions in Discrete Linear Temporal Logic.V. V. Rybakov - 2005 - Journal of Symbolic Logic 70 (4):1137 - 1149.
    We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. (...)
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  • Logics with the universal modality and admissible consecutions.Rybakov Vladimir - 2007 - Journal of Applied Non-Classical Logics 17 (3):383-396.
    In this paper1 we study admissible consecutions in multi-modal logics with the universal modality. We consider extensions of multi-modal logic S4n augmented with the universal modality. Admissible consecutions form the largest class of rules, under which a logic is closed. We propose an approach based on the context effective finite model property. Theorem 7, the main result of the paper, gives sufficient conditions for decidability of admissible consecutions in our logics. This theorem also provides an explicit algorithm for recognizing such (...)
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