An Event-Based Fragment of First-Order Logic over Intervals

Abstract
We consider a new fragment of first-order logic with two variables. This logic is defined over interval structures. It constitutes unary predicates, a binary predicate and a function symbol. Considering such a fragment of first-order logic is motivated by defining a general framework for event-based interval temporal logics. In this paper, we present a sound, complete and terminating decision procedure for this logic. We show that the logic is decidable, and provide a NEXPTIME complexity bound for satisfiability. This result shows that even a simple decidable fragment of first-order logic has NEXPTIME complexity
Keywords Two variable fragments of first-order logic  Interval temporal logics  Decidability  Tableau methods
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    References found in this work BETA
    Erich Grädel (1999). On the Restraining Power of Guards. Journal of Symbolic Logic 64 (4):1719-1742.
    Michael Mortimer (1975). On Languages with Two Variables. Mathematical Logic Quarterly 21 (1):135-140.
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