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An Extension Rule Based First-Order Theorem Prover

  • Xia Wu
  • Jigui Sun
  • Kun Hou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4092)

Abstract

Methods based on resolution have been widely used for theorem proving since it was proposed. The extension rule (ER) method is a new method for theorem proving, which is potentially a complementary method to resolution-based methods. But the first-order ER approach is incomplete and not realized. This paper gives a complete first-order ER algorithm and describes the implementation of a theorem prover based on it and its application to solving some planning problems. We also report the preliminary computational results on first-order formulation of planning problems.

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References

  1. 1.
    Lin, H., Sun, J.G., Zhang, Y.M.: Theorem proving based on extension rule. Journal of Automated Reasoning 31, 11–21 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Wu, X., Sun, J.G., Lu, S., Yin, M.H.: Propositional extension rule with reduction. International Journal of Computer Science and Network Security 6, 190–195 (2006)Google Scholar
  3. 3.
    Wu, X., Sun, J.G., Lu, S., Li, Y., Meng, W.: Improved propositional extension rule. In: Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.) RSKT 2006. LNCS, vol. 4062, pp. 592–597. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Wu, X., Sun, J.G., Hou, K.: Extension rule in first order logic. In: Proceeding of 5th International Conference on Cognitive Informatics (ICCI 2006), Beijing, China (to appear, 2006)Google Scholar
  5. 5.
    Chu, H., Plaisted, D.A.: Semantically Guided First-Order Theorem Proving Using Hyper-Linking. In: Proceeding of 12th Conference on Automated Deduction, Nancy, France, pp. 192–206 (1994)Google Scholar
  6. 6.
    Paramasivam, M., Plaisted, A.D.: A replacement rule theorem prover. Journal of Automated Reasoning 18, 221–226 (1997)CrossRefGoogle Scholar
  7. 7.
    Jeroslow, R.G.: Computation-oriented reductions of predicate to propositional logic. Decision Support Systems 4, 183–197 (1988)CrossRefGoogle Scholar
  8. 8.
    Chang, C., Lee, R.C.: Symbolic logic and mechanical theorem proving. Academic Press, London (1973)zbMATHGoogle Scholar
  9. 9.
    Kautz, H., Selman, B.: Planning as satisfiability. In: Proceeding of the 10th European Conference on Artificial Intelligence, Vienna, Austria, pp. 359–363 (1992)Google Scholar
  10. 10.
    Wu, X., Sun, J.G., Feng, S.S.: Destructive extension rule in modal logic K. In: Proceeding of International Conference of Computational Methods, Singapore (2004)Google Scholar
  11. 11.
    Wu, X., Sun, J.G., Lin, H., Feng, S.S.: Modal extension rule. Process In Natural Science, China 6, 550–558 (2005)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xia Wu
    • 1
    • 2
  • Jigui Sun
    • 1
    • 2
  • Kun Hou
    • 1
    • 2
    • 3
  1. 1.College of Computer Science and TechnologyJilin UniversityChangchunChina
  2. 2.Key Laboratory of Symbolic Computation and Knowledge Engineer of Ministry of EducationChangchunChina
  3. 3.College of Computer Science and TechnologyNortheast Normal UniversityChangchunChina

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