Extended asp tableaux and rule redundancy in normal logic programs1

  • Authors:

  • Matti JÄrvisalo;Emilia Oikarinen

  • Affiliations:

  • Helsinki university of technology (tkk), department of information and computer science, p.o. box 5400, fi-02015 tkk, finland (e-mail: matti.jarvisalo@tkk.fi, emilia.oikarinen@tkk.fi);Helsinki university of technology (tkk), department of information and computer science, p.o. box 5400, fi-02015 tkk, finland (e-mail: matti.jarvisalo@tkk.fi, emilia.oikarinen@tkk.fi)

  • Venue:
  • Theory and Practice of Logic Programming
  • Year:
  • 2008

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Abstract

We introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in the work by Gebser and Schaub (Tableau calculi for answer set programming. In Proceedings of the 22nd International Conference on Logic Programming (ICLP 2006), S. Etalle and M. Truszczynski, Eds. Lecture Notes in Computer Science, vol. 4079. Springer, 11–25) with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the relationship of Extended ASP Tableaux with the Extended Resolution proof system defined by Tseitin for sets of clauses, and separate Extended ASP Tableaux from ASP Tableaux by giving a polynomial-length proof for a family of normal logic programs {Φn} for which ASP Tableaux has exponential-length minimal proofs with respect to n. Additionally, Extended ASP Tableaux imply interesting insight into the effect of program simplification on the lengths of proofs in ASP. Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving.