Conceptual logic programs

Open answer set programming (OASP) solves the lack of modularity in closed world answer set programming by allowing for the grounding of logic programs with an arbitrary non-empty countable superset of the program’s constants. However, OASP is, in general, undecidable: the undecidable domino problem can be reduced to it. In order to regain decidability, we restrict the shape of logic programs, yielding conceptual logic programs (CoLPs). CoLPs are logic programs with unary and binary predicates (possibly inverted) where rules have a tree shape. Decidability of satisfiability checking of predicates w.r.t. CoLPs is shown by a reduction to non-emptiness checking of two-way alternating tree automata. We illustrate the expressiveness of CoLPs by simulating the description logic $\mathcal{SHIQ}$. CoLPs thus integrate, in one unifying framework, the best of both the logic programming paradigm (a flexible rule-based representation and nonmonotonicity by means of negation as failure) and the description logics paradigm (decidable open domain reasoning).

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