Hodkinson, I.M. and Wolter, F. and Zakharyaschev, Michael (2002) Decidable and undecidable fragments of first-order branching temporal logics. In: UNSPECIFIED (ed.) LICS 2002: 17th IEEE Symposium on Logic in Computer Science. IEEE Computer Society, pp. 393-402. ISBN 9780769514839.
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*-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'-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.
Metadata
| Item Type: | Book Section |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hall |
| Date Deposited: | 08 Nov 2021 14:04 |
| Last Modified: | 09 Aug 2023 12:52 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/46626 |
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