Reconciling description logics and rules

Abstract

Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and rules. Developing a formalism that integrates DLs and rules would be a natural outcome of a large body of research in knowledge representation and reasoning of the last two decades; however, achieving this goal is very challenging and the approaches proposed thus far have not fully reached it. In this paper, we present a hybrid formalism of MKNF + knowledge bases, which integrates DLs and rules in a coherent semantic framework. Achieving seamless integration is nontrivial, since DLs use an open-world assumption, while the rules are based on a closed-world assumption. We overcome this discrepancy by basing the semantics of our formalism on the logic of minimal knowledge and negation as failure (MKNF) by Lifschitz. We present several algorithms for reasoning with MKNF + knowledge bases, each suitable to different kinds of rules, and establish tight complexity bounds.

Extending Logic Programs with Description Logic Expressions for the Semantic Web

“…Like the FLP-reduct based semantics for DL-programs [13], this FLP-reduct based semantics for disjunctive DL-programs yields answer sets that are minimal but not necessarily well-supported models. Extensions of logic programs with DL expressions, such as DL-programs, DL+log, disjunctive DL-programs, and normal DL logic programs, are different in fundamental ways from embeddings of rules and DLs into some unifying logic formalisms, such as the embedding [1] to first-order autoepistemic logic [19] and the embedding [5] to the logic of Minimal Knowledge and Negation as Failure (MKNF) [20]. The two embeddings employ modal logics and transform rules Π and DL axioms L to autoepistemic (resp.…”

“…Ontologies describe terminological knowledge and rules model constraints and exceptions over the ontologies. Since the two components provide complementary descriptions of the same problem domain, they are supposed to be integrated in some ways (e.g., [1][2][3][4][5][6]; see [7] for a survey). The core of the Web ontology language OWL (more recently, OWL2) [8,9] is description logics (DLs) [10] and thus in this paper we assume an ontology is represented as a knowledge base in DLs.…”

A Approach to Clinical Proteomics Data Quality Control and Import

“…They structure, control and influence a system ( [12,22]). Recent works have shown the benefits of rules for Semantic Web ( [17,14]). In our approach we focus on rules for defining new part of knowledge that are not directly modeled in the ontology.…”

Uniform Evaluation of Nonmonotonic DL-Programs

“…In this context, the issue of combining rules and ontologies has been considered in a number of works; see [12,41,15] for some recent surveys. Among several approaches, loose coupling of rules and ontologies is one which aims at combining respective knowledge bases by means of a clean interfacing semantics, in which roughly speaking inferences are mutually exchanged such that the one knowledge base takes the imported information into account, and exports in turn conclusions to the other knowledge base.…”

“…For example, an exponential blowup of the DL-Lite rewriting in [8], which is prohibitive in some cases, can be mitigated [45] or avoided using other notions of rewritings [36]. As for items 1 and 2, embeddings of dl-programs into various well-known nonmonotonic logics have been studied, among them Autoepistemic Logic [13], Equilibrium Logic [21] (a logic-based version of Answer Set Semantics), Reiter's Default Logic [53], and MKNF [41]; however, these works targeted more semantic aspects than evaluation.…”