A New Method for Computing Preferred Extensions

Preferred semantics is one of the most important semantics in abstract argumentation. This paper designed a new algorithm, named ACPE, for computing preferred extensions based on SAT approach. Firstly, Algorithm ACPE searches for admissible extensions by converting admissible semantic into CNF formula and invoking SAT solver to solve this formula. After finding a new admissible extension, ACPE will get a complete extension by a strategy of expanding, after which ACPE adds a constraint formulae to the CNF formulae to avoid any subset of this extension to be found in searching for a new admissible extension. ACPE execute the above procedure repeatedly until it cannot find any admissible extensions by calling SAT solver. At last, ACPE found all maximum complete extensions or, that is to say, preferred extensions. Through theoretical analysis, this paper proved the correctness and completeness of ACPE. To analyze the performance of ACPE, we compared it with other three solvers, Cegartix, ArgSemSAT and CoQuiAAS, ranking the top three fast solver of computing enumeration reasoning problems for preferred semantics in international competition ICCMA'15. The result of experiment shows that the efficiency of ACPE is similar with ArgSemSAT and Cegartix but weaker than CoQuiAAS when solving easy problems; when it comes to hard problem, ACPE is generally better than ArgSemSAT and CoQuiAAS, and better than Cegartix for most instances.