José Júlio Alferes

TheRuleInterchangeFormatProductionRuleDialect(RIF- PRD) is a W3C Recommendation to define production rules for the Semantic Web, whose semantics is defined operationally via labeled ter- minal transition systems.
In this paper, we introduce a declarative logical characterization of the full default semantics of RIF-PRD based on Answer Set Programming (ASP), including matching, conflict resolution and acting.
Our proposal to the semantics of RIF-PRD enjoys several features. Being based on ASP, it enables a straightforward integration with Logic Programming rule based technology, namely for reasoning and acting with ontologies. Then, its full declarative logical character facilitates the in- vestigation of formal properties of RIF-PRD itself. Furthermore, it turns out that our characterization based on ASP is flexible enough so that new conflict resolution semantics for RIF-PRD can easily be defined and encoded. Finally, it immediately serves as the declarative specification of an implementation, whose prototype we developed.

Ontologies and rules are usually loosely coupled in knowledge rep- resentation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One ex- ception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the prac- tical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general Oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we pro- vide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF (ALCQ) theory.

Traditionally, a logic program is built up to reason about atomic first-order formulas. The key idea of parametrized logic program- ming is that, instead of atomic first-order formulas, a parametrized logic program reasons about formulas of a given parameter logic. Of course, the main challenge is to define the semantics of such general programs. In this work we introduce the novel definitions along with some motivating examples. This approach allows us to prove general results that can be instantiated for every particular choice of the parameter logic. Impor- tant general results we can prove include the existence of semantics and the alternating fix-point theorem of well-founded semantics. To reenforce the soundness of our general framework we show that some known approaches in the literature of logic programming, such as paraconsistent answer-sets and the MKNF semantics for hybrid knowledge bases, are obtained as particular choices of the parameter logic.

A general top-down algorithmization for the Well-Founded MKNF Semantics - a semantics for combining rules and
ontologies - was recently defined based on an extension of SLG resolution for Logic Programming with an abstract oracle to the parametric ontology language. Here we provide a concrete oracle with practical usage, namely for EL+ which is tractable for reasoning tasks like subsumption. We show that the defined oracle remains tractable
(wrt. data complexity) so that the combined (query-driven) approach of non-monotonic rules with that oracle is tractable as well.

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