Decidable and Undecidable Fragments of First-Order Branching Temporal Logics

Authors:
Ian M. Hodkinson;Frank Wolter;Michael Zakharyaschev
Affiliations:
-;-;-
Venue:
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Year:
2002

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Abstract

In this paper we analyze the decision problem for fragments of first-order extensions of branching time temporal logics such as computational tree logics CTL and CTL * or Prior's Ockhamist logic of historical necessity. On the one hand, we show that the one-variable fragments of logics like first-order CTL * 驴 such as the product of propositional CTL * with simple propositional modal logic S5, or even the one-variable bundled first-order temporal logic with sole temporal operator some time in the future' 驴 are undecidable. On the other hand, it is proved that by restricting applications of first-order quantifiers to state (i.e.,path-independent) formulas, and applications of temporal operators and path quantifiers to formulas with at most one free variable, we can obtain decidable fragments. The positive decidability results can serve as a unifying framework for devising expressive and effective time-dependent knowledge representation formalisms, e.g., temporal description or spatio-temporal logics.