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Journal of Logic, Language and Information

, Volume 20, Issue 1, pp 49–68 | Cite as

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

  • Savas KonurEmail author
Article

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

  1. Andreka, H., van Benthem, J., & Nemeti, I. (1996). Modal languges and Bounded Fragments of Predicate Logic. Research Report ML-96-03, IILC.Google Scholar
  2. Dechter R., Meiri I., Pearl J. (1991) Temporal constraint networks. Artificial Intelligence 49: 61–95CrossRefGoogle Scholar
  3. Goranko V., Montanari A., Sciavicco G. (2003) Propositional interval neighborhood temporal logics. Journal of Universal Computer Science 9(9): 1137–1167Google Scholar
  4. Goranko V., Montanari A., Sciavicco G., Sala P. (2006) A general Tableau method for propositional interval temporal logics: Theory and implementation. Journal of Applied Logic 4(3): 305–330CrossRefGoogle Scholar
  5. Grädel E. (1999) On the restraining power of guards. Journal of Symbolic Logic 64: 1719–1742CrossRefGoogle Scholar
  6. Grädel E., Kolaitis P., Vardi M. (1997) On the decision problem for two-variable first-order logic. Bulletin of Symbolic Logic 3: 53–69CrossRefGoogle Scholar
  7. Grädel E., Otto M. (1999) On logics with two variables. Theoretical Computer Science 224: 73–113CrossRefGoogle Scholar
  8. Halpern J.Y., Shoham Y. (1991) A propositional modal logic of time intervals. Journal of the ACM 38(4): 935–962CrossRefGoogle Scholar
  9. Konur S. (2008) An interval logic for natural language semantics. Advances in Modal Logic 7: 177–191Google Scholar
  10. Mortimer M. (1975) On languages with two variables. Zeitschr. f. math. Logik u. Grundlagen d. Math. 21: 135–140CrossRefGoogle Scholar
  11. Moszkowski, B. (1983). Reasoning about digital circuits. Stanford University: PhD Thesis, Department of Computer Science.Google Scholar
  12. Otto M. (2001) Two variable first-order logic over ordered domains. Journal of Symbolic Logic 66(2): 685–702CrossRefGoogle Scholar
  13. Pratt-Hartmann I. (2005) Temporal prepositions and their logic. Artificial Intelligence 166(1–2): 1–36CrossRefGoogle Scholar
  14. van Benthem, J. (1997). Dynamic Bits and Pieces. Research Report, ILLC.Google Scholar
  15. Venema Y. (1991) A modal logic for choppping intervals. Journal of Logic and Computation 1: 453–476CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of LiverpoolLiverpoolUK

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