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On the Expressive Power of First Order-Logic Extended with Allen’s Relations in the Strict Case

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Advances in Artificial Intelligence (CAEPIA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7023))

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Abstract

We consider the languages of first order-logic (with equality) extended with Allen’s relations for temporal intervals. We give a complete classification of such languages in terms of relative expressive power, thus determining how many, and which, are the intrinsically different extensions of first-order logic with one or more of Allen’s relations. Classifications are obtained for three different classes of interval structures, namely those based on arbitrary, discrete, and dense linear orders. The strict semantics (where point-intervals are excluded) is assumed throughout.

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References

  1. Allen, J.F., Hayes, P.J.: A common-sense theory of time. In: Proceedings of the 9th International Joint Conference on Artificial Intelligence, pp. 528–531. Morgan Kaufmann (1985)

    Google Scholar 

  2. Allen, J.F.: Maintaining knowledge about temporal intervals. Communications of the ACM 26, 832–843 (1983)

    Article  MATH  Google Scholar 

  3. Coetzee, C.J.: Representation theorems for classes of interval structures. Master’s thesis, Department of Mathematics, University of Johannesburg (2009)

    Google Scholar 

  4. Goranko, V., Montanari, A.: Sciavicco G. Propositional interval neighborhood temporal logics. Journal of Universal computer science 9(9), 1137–1167 (2003)

    MathSciNet  Google Scholar 

  5. Goranko, V., Montanari, A., Sciavicco, G.: A road map of interval temporal logics and duration calculi. Journal of Applied Non-Classical Logics 14(1-2), 9–54 (2004)

    Article  MATH  Google Scholar 

  6. Ladkin, P.: The Logic of Time Representation. PhD thesis, University of California, Berkeley (1978)

    Google Scholar 

  7. van Benthem, J.F.A.K.: The logic of time. Synthese Library, vol. 156. D. Reidel Publishing Co., Dordrecht (1983); A model-theoretic investigation into the varieties of temporal ontology and temporal discourse

    Book  MATH  Google Scholar 

  8. Venema, Y.: Expressiveness and completeness of an interval tense logic. Notre Dame Journal of Formal Logic 31(4), 529–547 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Johannesburg, Johannesburg, South Africa

    Willem Conradie

  2. Department of Information, Engineering and Communications, University of Murcia, Murcia, Spain

    Guido Sciavicco

Authors
  1. Willem Conradie
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  2. Guido Sciavicco
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Editor information

Editors and Affiliations

  1. Computer Science School, University of the Basque Country, Pº Manuel de Lardizabal 1, 20018, Donostia-San Sebastian, Spain

    Jose A. Lozano

  2. Computing Systems Department, University of Castilla-La Mancha, Campus Universitario s/n, 02071, Albacete, Spain

    José A. Gámez

  3. Dep. Statistics, O.R. and Computation, University of La Laguna, 38271, La Laguna, S.C. Tenerife, Spain

    José A. Moreno

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© 2011 Springer-Verlag Berlin Heidelberg

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Conradie, W., Sciavicco, G. (2011). On the Expressive Power of First Order-Logic Extended with Allen’s Relations in the Strict Case. In: Lozano, J.A., Gámez, J.A., Moreno, J.A. (eds) Advances in Artificial Intelligence. CAEPIA 2011. Lecture Notes in Computer Science(), vol 7023. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25274-7_18

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  • DOI: https://doi.org/10.1007/978-3-642-25274-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25273-0

  • Online ISBN: 978-3-642-25274-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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