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Simplifying Logic Programs Under Answer Set Semantics

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Logic Programming (ICLP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3132))

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Abstract

Now that answer set programming has emerged as a practical tool for knowledge representation and declarative problem solving there has recently been a revival of interest in transformation rules that allow for programs to be simplified and perhaps even reduced to programs of ‘lower’ complexity. Although it has been known for some that there is a maximal monotonic logic, denoted by N 5, with the property that its valid (equivalence preserving) inference rules provide valid transformations of programs under answer set semantics, with few exceptions this fact has not really been exploited in the literature. The paper studies some new transformation rules using N 5-inference to simplify extended disjunctive logic programs known to be strongly equivalent to programs with nested expressions.

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References

  1. Avellone, A., Ferrari, M., Miglioli, P.: Duplication-Free Tableau Calculi and Related Cut- Free Sequent Calculi for the Interpolable Propositional Intermediate Logics. Logic Journal of the IGPL 7(4), 447–480 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Balduccini, M., Gelfond, M., Watson, R., Noguiera, M.: The USA-Advisor: A case study in answer set planning. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, p. 439. Springer, Heidelberg (2001)

    Google Scholar 

  3. Baral, C.: Knowlewdge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  4. Brass, S., Dix, J.: Semantics of (Disjunctive) Logic Programs Based on Partial Evaluation. Journal of Logic Programming 40(1), 1–46 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Calimeri, F., Galizia, S., Ruffolo, M., Rullo, P.: Enhancing Disjunctive Logic Programming for Ontology Specification. In: Proceedings AGP 2003 (2003)

    Google Scholar 

  6. van Dalen, D.: Intuitionistic logic. In: Handbook of Philosophical Logic, Dordrecht. Alternatives in Classical Logic, vol. III, D. Reidel Publishing Co. (1986)

    Google Scholar 

  7. van Dantzig, D.: On the Principles of Intuitionistic and Affirmative Mathematics. Indagationes Mathematicae 9, 506–517 (1947)

    Google Scholar 

  8. Dietrich, J.: Inferenzframes. Doctoral Dissertation, University of Leipzig (1995)

    Google Scholar 

  9. Dummett, M.: Elements of Intuitionism. Clarendon Press, Oxford (1977)

    MATH  Google Scholar 

  10. Eiter, T., Fink, M.: Uniform equivalence of logic programs under the stable model semantics. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 224–238. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Eiter, T., et al.: Simplifying Logic Programs under Uniform and Strong Equivalence. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 87–99. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Eiter, T., Gottlob, G.: On the Computational Cost of Disjunctive Logic Programming: Propositional Case. Annals of Mathematics and Artificial Intelligence 15(3-4), 289–323 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gödel, K.: Zum intuitionistischen aussagenkalkül. Anzeiger der Akademie der Wissenschaften Wien, mathematisch, naturwissenschaftliche Klasse 69, 65–66 (1932)

    Google Scholar 

  14. Gurevich, Y.: Intuitionistic logic with strong negation. Studia Logica 36(1-2), 49–59 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  15. Heyting: Die formalen regeln der intuitionistischen logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp. 42–56 (1930)

    Google Scholar 

  16. De Jongh, D., Hendriks, L.: Characterization of strongly equivalent logic programs in intermediate logics. Theory and Practice of Logic Programming 3(3), 259–270 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Janhunen, T.: On the Effect of Default Negation on the Expressiveness of Disjunctive Rules. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 93–106. Springer, Heidelberg (2001)

    Google Scholar 

  18. Janhumen, T., Niemelä, I., Seipel, D., Simons, P., You, J.-H.: Unfolding partiality and disjunctions in stable model semantics. CoRR: cs.AI/0303009 (March 2003)

    Google Scholar 

  19. Kracht, M.: On extensions of intermediate logics by strong negation. Journal of Philosophical Logic 27(1), 49–73 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  20. Leone, N., Pfeifer, G., Faber, W., Eiter, T.: G, Gottlob, S. Perri and F. Scarcello. The DLV System for Knowledge Representation and Reasoning. CoRR: cs.AI/0211004 (September 2003)

    Google Scholar 

  21. Lifschitz, V.: Foundations of Logic Programming. In: Brewka, G. (ed.) Principles of Knowledge Representation, pp. 69–128. CSLI Publications, Stanford (1996)

    Google Scholar 

  22. Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)

    Article  MathSciNet  Google Scholar 

  23. Lifschitz, V., Tang, L., Turner, H.: Nested Expressions in Logic Programs. Annals of Mathematics and Artificial Intelligence 25(3-4), 369–389 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  24. Mundici, D.: Satisfiability in Many-Valued Sentential Logic is NP-complete. Theoretical Computer Science 52(1-2), 145–153 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  25. Osorio, M., Navarro, J., Arrazola, J.: Equivalence in Answer Set Programming. In: Pettorossi, A. (ed.) LOPSTR 2001. LNCS, vol. 2372, pp. 57–75. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  26. Pearce, D.: Nonmonotonicity and Answer Set Inference. In: Marek, V.W., Truszczyński, M., Nerode, A. (eds.) LPNMR 1995. LNCS, vol. 928, pp. 372–387. Springer, Heidelberg (1995)

    Google Scholar 

  27. Pearce, D.: A new logical characterization of stable models and answer sets. In: Dix, J., Przymusinski, T.C., Moniz Pereira, L. (eds.) NMELP 1996. LNCS, vol. 1216, pp. 57–70. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  28. Pearce, D., de Guzmán, I.P., Valverde, A.: A tableau calculus for equilibrium entailment. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS, vol. 1847, pp. 352–367. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  29. Pearce, D., de Guzmán, I.P., Valverde, A.: Computing equilibrium models using signed formulas. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 688–702. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  30. Pearce, D., Tompits, H., Woltran, S.: Encodings for Equilibrium Logic and Logic Programs with Nested Expressions. In: Brazdil, P.B., Jorge, A.M. (eds.) EPIA 2001. LNCS (LNAI), vol. 2258, pp. 306–320. Springer, Heidelberg (2001)

    Google Scholar 

  31. Pearce, D., Sarsakov, V., Schaub, T., Tompits, H., Woltran, S.: A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 405–420. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  32. Pearce, D., Valverde, A.: Uniform Equivalence for Equilibrium Logic and Logic Programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 194–206. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  33. Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intellingence 138(1-2), 181–234 (2002)

    Article  MATH  Google Scholar 

  34. Turner, H.: Strong equivalence for logic programs and default theories (made easy). In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 81–92. Springer, Heidelberg (2001)

    Google Scholar 

  35. Vakarelov, D.: Notes on N-Lattices and Constructive Logic with Strong Negation. Studia Logica 36(1-2), 109–125 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  36. Vorob’ev, N.N.: A constructive propositional calculus with strong negation (in Russian). Doklady Akademii Nauk SSR 85, 465–468 (1952)

    MathSciNet  Google Scholar 

  37. Vorob’ev, N.N.: The problem of deducibility in constructive propositional calculus with strong negation (in Russian). Doklady Akademii Nauk SSR 85, 689–692 (1952)

    MathSciNet  Google Scholar 

  38. Wang, K., Zhou, L.: Comparisons and Computation of Well-founded Semantics for Disjunctive Logic Programs. ACM Transactions on Computational Logic (to appear)

    Google Scholar 

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Pearce, D. (2004). Simplifying Logic Programs Under Answer Set Semantics. In: Demoen, B., Lifschitz, V. (eds) Logic Programming. ICLP 2004. Lecture Notes in Computer Science, vol 3132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27775-0_15

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  • DOI: https://doi.org/10.1007/978-3-540-27775-0_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22671-0

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