A propositional theorem prover to solve planning and other problems

  • Authors:

  • Allen Van Gelder;Fumiaki Okushi

  • Affiliations:

  • Computer Science Department, 225 AS, University of California, Santa Cruz, CA 95064, USA E-mail: avg@cs.ucsc.edu, okushi@cs.ucsc.edu;Computer Science Department, 225 AS, University of California, Santa Cruz, CA 95064, USA E-mail: avg@cs.ucsc.edu, okushi@cs.ucsc.edu

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 1999

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Abstract

Classical STRIPS‐style planning problems are formulated as theorems to be proven from a new point of view: that the problem is not solvable. The result for a refutation‐based theorem prover may be a propositional formula that is to be proven unsatisfiable. This formula is identical to the formula that may be derived directly by various “SAT compilers”, but the theorem‐proving view provides valuable additional information not in the formula, namely, the theorem to be proven. Traditional satisfiability methods, most of which are based on model search, are unable to exploit this additional information. However, a new algorithm called “Modoc” is able to exploit this information and has achieved performance comparable to the fastest known satisfiability methods, including stochastic search methods, on planning problems that have been reported by other researchers, as well as formulas derived from other applications. Unlike most theorem provers, Modoc performs well on both satisfiable and unsatisfiable formulas. Modoc works by a combination of back‐chaining from the theorem clauses and forward‐chaining on tractable subformulas. In some cases, Modoc is able to solve a planning problem without finding a complete assignment because the back‐chaining methodology is able to ignore irrelevant clauses. Although back‐chaining is well known in the literature, a high level of search redundancy existed in previous methods; Modoc incorporates a new technique called “autarky pruning”, which reduces search redundancy to manageable levels, permitting the benefits of back‐chaining to emerge, for certain problem classes. Experimental results are presented for planning problems and formulas derived from other applications.