Model-Intersection Problems and Their Solution Schema Based on Equivalent Transformation

  • Kiyoshi Akama
  • Ekawit Nantajeewarawat
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 631)


Model-intersection (MI) problems are a very large class of logical problems that includes many useful problem classes, such as proof problems on first-order logic and query-answering (QA) problems in pure Prolog and deductive databases. We propose a general schema for solving MI problems by equivalent transformation (ET), where problems are solved by repeated simplification. The correctness of this solution schema is shown. This general schema is specialized for formalizing solution schemas for QA problems and proof problems. The notion of a target mapping is introduced for generation of ET rules, allowing many possible computation procedures, for instance, computation procedures based on resolution and unfolding. This theory is useful for inventing solutions for many classes of logical problems.


Model-intersection problem Query-answering problem Equivalent transformation Problem solving 



This research was partially supported by JSPS KAKENHI Grant Numbers 25280078 and 26540110.


  1. 1.
    Akama, K., Nantajeewarawat, E.: Proving theorems based on equivalent transformation using resolution and factoring. In: Proceedings of the Second World Congress on Information and Communication Technologies, WICT 2012, Trivandrum, India, pp. 7–12 (2012)Google Scholar
  2. 2.
    Akama, K., Nantajeewarawat, E.: Embedding proof problems into query-answering problems and problem solving by equivalent transformation. In: Proceedings of the 5th International Conference on Knowledge Engineering and Ontology Development, Vilamoura, Portugal, pp. 253–260 (2013)Google Scholar
  3. 3.
    Akama, K., Nantajeewarawat, E.: Equivalent transformation in an extended space for solving query-answering problems. In: Nguyen, N.T., Attachoo, B., Trawiński, B., Somboonviwat, K. (eds.) ACIIDS 2014. LNCS (LNAI), vol. 8397, pp. 232–241. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-05476-6_24 CrossRefGoogle Scholar
  4. 4.
    Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook, 2nd edn. Cambridge University Press, Cambridge (2007)Google Scholar
  5. 5.
    Chang, C.L., Lee, R.C.T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, Cambridge (1973)zbMATHGoogle Scholar
  6. 6.
    Clark, K.L.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)CrossRefGoogle Scholar
  7. 7.
    Donini, F.M., Lenzerini, M., Nardi, D., Schaerf, A.: \({\cal{A}}{\cal{L}}\)-log: integrating datalog and description logics. J. Intell. Inf. Syst. 16, 227–252 (1998)CrossRefGoogle Scholar
  8. 8.
    Fitting, M.: First-Order Logic and Automated Theorem Proving, 2nd edn. Springer, Berlin (1996)CrossRefzbMATHGoogle Scholar
  9. 9.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of International Logic Programming Conference and Symposium, pp. 1070–1080. MIT Press (1988)Google Scholar
  10. 10.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9, 365–386 (1991)CrossRefzbMATHGoogle Scholar
  11. 11.
    Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Berlin (1987)CrossRefzbMATHGoogle Scholar
  12. 12.
    Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. ACM 12, 23–41 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Tessaris, S.: Questions and answers: reasoning and querying in description logic. Ph.D. thesis, Department of Computer Science, The University of Manchester, UK (2001)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Information Initiative CenterHokkaido UniversityHokkaidoJapan
  2. 2.Computer Science Program, Sirindhorn International Institute of TechnologyThammasat UniversityPathumthaniThailand

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