Dynamic and Static Symmetry Breaking in Answer Set Programming

Abstract

Many research works had been done in order to define a semantics for logic programs. The well know is the stable model semantics which selects for each program one of its canonical models. The stable models of a logic program are in a certain sens the minimal Herbrand models of its reduct programs. On the other hand, the notion of symmetry elimination had been widely studied in constraint programming and shown to be useful to increase the efficiency of the associated solvers. However symmetry in non monotonic reasoning still not well studied in general. For instance Answer Set Programming (ASP) is a very known framework but only few recent works on symmetry breaking are known in this domain. Ignoring symmetry breaking in the answer set systems could make them doing redundant work and lose on their efficiency. Here we study the notion of local and global symmetry in the framework of answer set programming. We show how local symmetries of a logic program can be detected dynamically by means of the automorphisms of its graph representation. We also give some properties that allow to eliminate theses symmetries in SAT-based answer set solvers and show how to integrate this symmetry elimination in these methods in order to enhance their efficiency.