Blocking and other enhancements for bottom-up model generation methods

  • Authors:

  • Peter Baumgartner;Renate A. Schmidt

  • Affiliations:

  • National ICT Australia (NICTA);The University of Manchester

  • Venue:
  • IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
  • Year:
  • 2006

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Abstract

In this paper we introduce several new improvements to the bottom-up model generation (BUMG) paradigm. Our techniques are based on non-trivial transformations of first-order problems into a certain implicational form, namely range-restricted clauses. These refine existing transformations to range-restricted form by extending the domain of interpretation with new Skolem terms in a more careful and deliberate way. Our transformations also extend BUMG with a blocking technique for detecting recurrence in models. Blocking is based on a conceptually rather simple encoding together with standard equality theorem proving and redundancy elimination techniques. This provides a general-purpose method for finding small models. The presented techniques are implemented and have been successfully tested with existing theorem provers on the satisfiable problems from the TPTP library.