Combining Rules and Ontologies via Parametrized Logic Programs

Parametrized logic programs are very expressive logic programs that generalize normal logic programs under the stable model semantics, by allowing complex formulas of a parameter logic to appear in the body and head of rules. In this paper we explore the use of description logics as parameter logics, and show the expressivity of this framework for combining rules and ontologies. Introduction Parametrized logic programming [Gonçalves and Alferes, 2010] was introduced as an extension of answer set programming [Gelfond and Lifschitz, 1988] with the motivation of providing a meaning to theories combining both logic programming connectives with other logical connectives, and allowing complex formulas using these connectives to appear in the head and body of a rule. The main idea is to fix a monotonic logic L, called the parameter logic, and build up logic programs using formulas of L instead of just atoms. The obtained parametrized logic programs have, therefore, the same structure of normal logic programs, being the only difference the fact that atomic symbols are replaced by formulas of L. When applying this framework, the choice of the parameter logic depends on the domain of the problem to be modeled. As examples, [Gonçalves and Alferes, 2010] shows how to obtain the answer-set semantics of logic programs with explicit negation, a paraconsistent version of it, and also the semantics of MKNF hybrid knowledge bases [Motik and Rosati, 2010], using an appropriate choice of the parameter logic. In [Gonçalves and Alferes, 2012] deontic logic programs are introduced using standard deontic logic [von Wright, 1951] as the parameter logic. Moreover, in [Gonçalves and Alferes, 2013] the decidability and implementation of parametrized logic was discussed. Parametrized logic programming can thus be seen as a framework which allows to add non-monotonic rule based reasoning on top of an existing (monotonic) language. This view is quite interesting, in particular in those cases where we already have a monotonic logic to model a problem, but we are still lacking some conditional or non-monotonic reasoning. In these situations, parametrized logic programming offers a modular framework for adding such conditional and non-monotonic reasoning, without having to give up of the monotonic logic at hand. In recent years, there has been a considerable amount of effort devoted to combining Description Logics (DLs) with logic programming non-monotonic rules – see, e.g., related work in [Eiter et al., 2008; Motik and Rosati, 2010]. In this paper we explore precisely the use of description logics as parameter logics, and show the expressivity of the resulting framework for combining rules and ontologies. Parametrized logic programs Parametrized logic programs are very expressive logic programs that generalize normal logic programs under the stable model semantics, by allowing complex formulas of a parameter logic to appear in the body and head of rules. In this section we introduce the syntax and semantics of normal parametrized logic programs [Gonçalves and Alferes, 2010].