Semantic Web Reasoning with Conceptual Logic Programs [chapter]

Stijn Heymans, Davy Van Nieuwenborgh, Dirk Vermeir
2004 Lecture Notes in Computer Science  
We extend Answer Set Programming with, possibly infinite, open domains. Since this leads, in general, to undecidable reasoning, we restrict the syntax of programs, while carefully guarding useful knowledge representation mechanisms such as negation as failure and inequalities. Reasoning with the resulting Conceptual Logic Programs can be reduced to finite, normal Answer Set Programming, for which reasoners are available. We argue that Conceptual Logic Programming is a useful tool for uniformly
more » ... epresenting and reasoning with both ontologies and rules on the Semantic Web, as they can capture a large fragment of the OWL DL ontology language, while extending it in various aspects. Using traditional ASP, grounding would yield the program which has a single answer set {¬Manager (felix )} such that one would wrongfully conclude that there are never managers or persons that drive big cars. We resolve this by introducing, possibly infinite, open domains. Under the open answer set semantics the example has an answer set (H = {felix , heather }, M = {¬Manager (felix ), Manager (heather ), bigCar (heather )}) where H is a universe for P 1 that extends the constants present in P 1 and M is an answer set of P 1 grounded with H. One would rightfully conclude that it is possible that there are persons that are managers and thus drive big cars. Note the use of disjunction and negation as failure in the head of Manager (X ) ∨ not Manager (X ) ← . Such rules will be referred to as free rules since they allow for the free introduction of literals; answer sets are, consequently, not subset minimal. The catch is that reasoning, i.e. satisfiability checking of a predicate, with open domains is, in general, undecidable. In order to regain decidability, we restrict the syntax of programs while retaining useful knowledge representation tools such as negation as failure and inequality. Moreover, the result, (local) Conceptual Logic Programs (CLPs), ensures a reduction of reasoning to finite, closed, ASP, making CLPs amenable for reasoning with existing answer set solvers. As opposed to the CLPs in [16, 15] , we support constants in this paper. Constants in a CLP have the effect that the tree-model property, a decidability indicator, is replaced by the more general forest-model property. Furthermore, [16, 15] characterized reasoning with CLPs by checking non-emptiness of two-way alternating tree-automata [31] . Although such automata are elegant theoretical tools, they are of little practical use, hence the importance of an identification of CLPs that can be reduced to traditional ASP. Conceptual logic programs prove to be suitable for Semantic Web reasoning, for we can simulate an expressive DL closely related to the ontology language OWL DL. Since CLPs, as a LP paradigm, are also a natural framework for representing rule-based knowledge, they present a unifying framework for reasoning with ontologies and rules. Some additional benefits of CLPs, compared with OWL DL, are their ability to close the domain at will and to succinctly represent knowledge that is not trivially expressible using OWL DL. Finally, several query problems, in the context of databases satisfying ontologies, can be stated as satisfiability problems w.r.t. CLPs and are consequently decidable. The remainder of the paper is organized as follows. In Section 2, we extend ASP with open domains, and in Section 3, we define (local) CLPs and reduce reasoning to normal ASP. In Section 4, we show the simulation of an expressive class of DLs and
doi:10.1007/978-3-540-30504-0_9 fatcat:lcsryatlbrgjrnqfa5ucndphxu