Modular Paracoherent Answer Sets

Abstract The answer set semantics may assign a logic program no model due to classic contradiction or cyclic negation. The latter can be remedied by resorting to 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. While SEQ -models have interesting properties, they 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 modeling and evaluating 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. Splitting SEQ -models does not make reasoning harder, except for deciding model existence in presence of constraints (without constraints, split SEQ -models always exist).

Authors

• Giovanni Amendola
• Thomas Eiter
• Nicola Leone

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