Integration of and a Solution for Proof Problems and Query-Answering Problems

  • Kiyoshi AkamaEmail author
  • Ekawit Nantajeewarawat
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 454)


Proof problems have long been the main target for logical problem solving. A problem in this class is a “yes/no” problem concerning with checking whether one logical formula is a logical consequence of another logical formula. Meanwhile, the importance of anther class of problems, query-answering problems (QA problems), has been increasingly recognized. A QA problem is an “all-answers finding” problem concerning with finding all ground instances of a query atomic formula that are logical consequences of a given logical formula. Several specific subclasses of QA problems have been addressed based on solution techniques for proof problems, without success of finding general solutions. In order to establish solution methods for proof problems and QA problems, we integrate these two classes of problems by embedding proof problems into QA problems. Construction of low-cost embedding mappings from proof problems to QA problems is demonstrated. By such embedding, proof problems can be solved using a procedure for solving QA problems. A procedure for solving QA problems based on equivalent transformation is presented. The presented work provides a new framework for integration of proof problems and QA problems and a solution for them by the general principle of equivalent transformation.


Query-answering problems Proof problems Equivalent transformation Solving logical problems 


  1. 1.
    Akama, K., Nantajeewarawat, E.: Meaning-preserving skolemization. In: 2011 International Conference on Knowledge Engineering and Ontology Development, Paris, France, pp. 322–327 (2011)Google Scholar
  2. 2.
    Akama, K., Nantajeewarawat, E.: Proving theorems based on equivalent transformation using resolution and factoring. In: 2nd World Congress on Information and Communication Technologies, Trivandrum, India, pp. 7–12 (2012)Google Scholar
  3. 3.
    Akama, K., Nantajeewarawat, E.: Embedding proof problems into query-answering problems and problem solving by equivalent transformation. Technical report, Hokkaido University, Sapporo, Japan (2013)Google Scholar
  4. 4.
    Beth, E.W.: Semantic Entailment and Formal Derivability. Noord-Hollandsche Uitg. Mij, Amsterdam (1955)Google Scholar
  5. 5.
    Chang, C.-L., Lee, R.C.-T.: Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York (1973)zbMATHGoogle Scholar
  6. 6.
    Fitting, M.: First-Order Logic and Automated Theorem Proving, 2nd edn. Springer, New York (1996)CrossRefzbMATHGoogle Scholar
  7. 7.
    Gallier, J.H.: Logic for Computer Science: Foundations of Automatic Theorem Proving. Wiley, New York (1986)zbMATHGoogle Scholar
  8. 8.
    Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)CrossRefzbMATHGoogle Scholar
  9. 9.
    Motik, B., Sattler, U., Studer, R.: Query answering for OWL-DL with rules. J. Web Semant. 3, 41–60 (2005)CrossRefGoogle Scholar
  10. 10.
    Newborn, M.: Automated Theorem Proving: Theory and Practice. Springer, New York (2000)Google Scholar
  11. 11.
    Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. ACM 12, 23–41 (1965)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Information Initiative CenterHokkaido UniversitySapporoJapan
  2. 2.Computer Science ProgramSirindhorn International Institute of Technology, Thammasat UniversityPathumthaniThailand

Personalised recommendations