Towards a unified model of search in theorem-proving: subgoal-reduction strategies

  • Authors:

  • Maria Paola Bonacina

  • Affiliations:

  • Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, I-37134 Verona, Italy

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2005

  • Labelled Clauses

    CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction

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Abstract

This paper advances the design of a unified model for the representation of search in first-order clausal theorem-proving, by extending to tableau-based subgoal-reduction strategies (e.g., model-elimination tableaux), the marked search-graph model, already introduced for ordering-based strategies, those that use (ordered) resolution, paramodulation/superposition, simplification, and subsumption. The resulting analytic marked search-graphs subsume AND-OR graphs, and allow us to represent those dynamic components, such as backtracking and instantiation of rigid variables, that have long been an obstacle to modelling subgoal-reduction strategies properly. The second part of the paper develops for analytic marked search-graphs the bounded search spaces approach to the analysis of infinite search spaces. We analyze how tableau inferences and backtracking affect the bounded search spaces during a derivation. Then, we apply this analysis to measure the effects of regularity and lemmatization by folding-up on search complexity, by comparing the bounded search spaces of strategies with and without these features. We conclude with a discussion comparing the marked search-graphs for tableaux, linear resolution, and ordering-based strategies, showing how this search model applies across these classes of strategies.