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  1. Discrete Linear Temporal Logic with Current Time Point Clusters, Deciding Algorithms.V. Rybakov - 2008 - Logic and Logical Philosophy 17 (1-2):143-161.
    The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules in special reduced (...)
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  • KD is Nullary.Philippe Balbiani & Çiğdem Gencer - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):196-205.
    In the ordinary modal language, KD is the modal logic determined by the class of all serial frames. In this paper, we demonstrate that KD is nullary.
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  • Remarks About the Unification Type of Several Non-Symmetric Non-Transitive Modal Logics.Philippe Balbiani - 2019 - Logic Journal of the IGPL 27 (5):639-658.
    The problem of unification in a normal modal logic $L$ can be defined as follows: given a formula $\varphi$, determine whether there exists a substitution $\sigma$ such that $\sigma $ is in $L$. In this paper, we prove that for several non-symmetric non-transitive modal logics, there exists unifiable formulas that possess no minimal complete set of unifiers.
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  • Decidability: Theorems and Admissible Rules.Vladimir Rybakov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):293-308.
    The paper deals with a temporal multi-agent logic TMAZ, which imitates taking of decisions based on agents' access to knowledge by their interaction. The interaction is modelled by possible communication channels between agents in special temporal Kripke/hintikka-like models. The logic TMAZ distinguishes local and global decisions-making. TMAZ is based on temporal Kripke/hintikka models with agents' accessibility relations defined on states of all possible time clusters C. The main result provides a decision algorithm for TMAZ. This algorithm also solves the satisfiability (...)
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  • Logics of Kripke Meta-Models.Sergey Babenyshev & Vladimir Rybakov - 2010 - Logic Journal of the IGPL 18 (6):823-836.
    This paper introduces and studies a new type of logical construction, which allows to combine various non-classical propositional logics with the temporal or modal background. The possible candidates include a number of epistemic, multi-agent, deontological and other well-studied logics. In this construction, that we call refinement, the Kripke structure of a chosen Kripke complete logic is imposed on clusters of the background transitive frame. Refinements fit in a wider framework of fibred logics, while having some unique features. First of all, (...)
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  • Linear Temporal Logic with Until and Next, Logical Consecutions.V. Rybakov - 2008 - Annals of Pure and Applied Logic 155 (1):32-45.
    While specifications and verifications of concurrent systems employ Linear Temporal Logic , it is increasingly likely that logical consequence in image will be used in the description of computations and parallel reasoning. Our paper considers logical consequence in the standard image with temporal operations image and image . The prime result is an algorithm recognizing consecutions admissible in image, so we prove that image is decidable w.r.t. admissible inference rules. As a consequence we obtain algorithms verifying the validity of consecutions (...)
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  • Projective Formulas and Unification in Linear Temporal Logic LTLU.V. Rybakov - 2014 - Logic Journal of the IGPL 22 (4):665-672.