A Partial Instantiation based First Order Theorem Prover (original) (raw)
1998, Tepper School of Business
Satis ability algorithms for propositional logic have improved enormously in recent years. This increases the attractiveness of satis ability methods for rst order logic that reduce the problem to a series of ground-level satis ability problems. Partial Instantiation for rst order satis ability di ers radically from standard resolution based methods. Two approaches to partial instantiation based rst order theorem provers have been studied by R. Jeroslow 10] and by Plaisted and Zhu 14]. Hooker and Rago 8, 9] have described improvements of Jeroslow's approach by a) extending it to logic with functions, b) accelerating it through use of satis ers, as introduced by Gallo and Rago 6] and c) simplifying it to obtain further speedup. The correctness of the Partial Instantiation algorithms described here for full rst-order logic with functions as well as termination on unsatis able formulas are shown in 9]. This paper describes the implementation of a theorem prover based on the primal algorithm and its application to solving planning problems. We obtained improved e ciency by incorporating incrementality into the primal algorithm (incremental blockage testing). This extended abstract describes the Partial Primal Instantiation algorithm, its implementation and preliminary results on rst order formulation of planning problems.
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