Dealing with Incoherence in ASP: Split Semi-Equilibrium Semantics

The answer set semantics may assign a logic program no model due to classic contradiction or cyclic negation. The latter can be remedied by a paracoherent semantics given by semi-equilibrium (SEQ) models, which are 3-valued interpretations that generalize the logical reconstruction of answer sets given by equilibrium models. However SEQ-models miss modularity in the rules, such that a natural modular (bottom up) evaluation of programs is hindered. We thus refine SEQ-models using splitting sets, the major tool for modularity in answer set programs. We consider canonical models that are independent of any particular splitting sequence from a class of splitting sequences, and present two such classes whose members are efficiently recognizable. Split SEQ-models does not make reasoning harder, except for deciding model existence in presence of constraints.