Consistency Property of Finite FC-Normal Logic Programs

Marek＇s forward-chaining construction is one of the important techniques for investigating the non-monotonic reasoning. By introduction of consistency property over a logic program, they proposed a class of logic programs, FC-normal programs, each of which has at least one stable model. However, it is not clear how to choose one appropriate consistency property for deciding whether or not a logic program is FC-normal. In this paper, we firstly discover that, for any finite logic programⅡ, there exists the least consistency property LCon（Ⅱ） overⅡ, which just depends onⅡitself, such that, Ⅱ is FC-normal if and only ifⅡ is FC-normal with respect to （w.r.t.） LCon（Ⅱ）. Actually, in order to determine the FC-normality of a logic program, it is sufficient to check the monotonic closed sets in LCon（Ⅱ） for all non-monotonic rules, that is LFC（Ⅱ）. Secondly, we present an algorithm for computing LFC（Ⅱ）. Finally, we reveal that the brave reasoning task and cautious reasoning task for FC-normal logic programs are of the same difficulty as that of normal logic programs.