A New Method for Computing Stable Models in Logic Programming

Abstract

In this work, we introduce a new method for searching stable models of logical programs. This method is based on a relatively new semantics that has not been exploited yet. This semantics captures and extends that one of the stable models (Gelfond et al., 1988) and offers a new alternative to implement ASP solvers. The proposed method performs a DPLL enumerative process that is adapted to Answer Set Programming (ASP) framework according to the used semantics. This method has the advantage to use a Horn clause representation having the same size as the input logic program has constant spatial complexity. It avoids the workload induced by the loop management from which suffer most of the ASP solvers based on the Clark completion. Moreover, the enumeration is done on a restricted set of literals called the strong back-door (STB) of the considered logic program. This reduces the algorithm time complexity which is in theory a function of the size of the STB set. We also introduced new inference rules that the method uses to prune its search tree and hence reduces its size in practice. We implemented the proposed method and applied it to enumerate the stable models of some combinatorial problems. The method is compared to other known systems and the obtained results show that our approach is a good alternative for designing ASP solvers.