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Using model generation theorem provers for the computation of answer sets

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2009
Sabuncu, Orkunt
Answer set programming (ASP) is a declarative approach to solving search problems. Logic programming constitutes the foundation of ASP. ASP is not a proof-theoretical approach where you get solutions by answer substitutions. Instead, the problem is represented by a logic program in such a way that models of the program according to the answer set semantics correspond to solutions of the problem. Answer set solvers (Smodels, Cmodels, Clasp, and Dlv) are used for finding answer sets of a given program. Although users can write programs with variables for convenience, current answer set solvers work on ground logic programs where there are no variables. The grounding step of ASP generates a propositional instance of a logic program with variables. It may generate a huge propositional instance and make the search process of answer set solvers more difficult. Model generation theorem provers (Paradox, Darwin, and FM-Darwin) have the capability of producing a model when the first-order input theory is satisfiable. This work proposes the use of model generation theorem provers as computational engines for ASP. The main motivation is to eliminate the grounding step of ASP completely or to perform it more intelligently using the model generation system. Additionally, regardless of grounding, model generation systems may display better performance than the current solvers. The proposed method can be seen as lifting SAT-based ASP, where SAT solvers are used to compute answer sets, to the first-order level for tight programs. A completion procedure which transforms a logic program to formulas of first-order logic is utilized. Besides completion, other transformations which are necessary for forming a firstorder theory suitable for model generation theorem provers are investigated. A system called Completor is implemented for handling all the necessary transformations. The empirical results demonstrate that the use of Completor and the theorem provers together can be an e ective way of computing answer sets. Especially, the run time results of Paradox in the experiments has showed that using Completor and Paradox together is favorable compared to answer set solvers. This advantage has been more clearly observed for programs with large propositional instances, since grounding can be a bottleneck for such programs.