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  1. Linear-Time Temporal Logics with Presburger Constraints: An Overview ★.Stéphane Demri - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):311-347.
    We present an overview of linear-time temporal logics with Presburger constraints whose models are sequences of tuples of integers. Such formal specification languages are well-designed to specify and verify systems that can be modelled with counter systems. The paper recalls the general framework of LTL over concrete domains and presents the main decidability and complexity results related to fragments of Presburger LTL. Related formalisms are also briefly presented.
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  • Complexity of Monodic Guarded Fragments Over Linear and Real Time.Ian Hodkinson - 2006 - Annals of Pure and Applied Logic 138 (1):94-125.
    We show that the satisfiability problem for the monodic guarded, loosely guarded, and packed fragments of first-order temporal logic with equality is 2Exptime-complete for structures with arbitrary first-order domains, over linear time, dense linear time, rational number time, and some other classes of linear flows of time. We then show that for structures with finite first-order domains, these fragments are also 2Exptime-complete over real number time and hence over most of the commonly used linear flows of time, including the natural (...)
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  • The Monodic Fragment of Propositional Term Modal Logic.Anantha Padmanabha & R. Ramanujam - 2019 - Studia Logica 107 (3):533-557.
    We study term modal logics, where modalities can be indexed by variables that can be quantified over. We suggest that these logics are appropriate for reasoning about systems of unboundedly many reasoners and define a notion of bisimulation which preserves propositional fragment of term modal logics. Also we show that the propositional fragment is already undecidable but that its monodic fragment is decidable, and expressive enough to include interesting assertions.
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  • Non-Finitely Axiomatisable Two-Dimensional Modal Logics.Agi Kurucz & Sérgio Marcelino - 2012 - Journal of Symbolic Logic 77 (3):970-986.
    We show the first examples of recursively enumerable (even decidable) two-dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.
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  • The Serializability Problem for a Temporal Logic of Transaction Queries.Walter Hussak - 2008 - Journal of Applied Non-Classical Logics 18 (1):67-78.
    We define the logic FOTLT, to be a monadic monodic fragment of first-order linear temporal logic, with 2n propositions representing the read and write steps of n two-step concurrent database transactions and a time-dependent predicate representing queries giving the sets of data items accessed by those read and write steps at given points in time. The models of FOTLT contain interleaved sequences of the steps of infinitely many occurrences of the n transactions accessing unlimited data over time. A property of (...)
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