Equality-friendly well-founded semantics and applications to description logics

We tackle the problem of defining a well-founded semantics (WFS) for Datalog rules with existentially quantified variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratified nonmonotonic nega- tion in rule bodies, and we define a WFS for this generalization via guarded fixed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise defi- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering

Upward Refinement for Conceptual Blending in Description Logic — An ASP-based Approach and Case Study in EL++—

Conceptual blending is understood to be a process that serves a variety of cognitive purposes, including creativity, and has been highly influential in cognitive linguistics. In this line of thinking, human creativity is modeled as a blending process that takes different mental spaces as input and combines them into a new mental space, called a blend. According to this form of combinatorial creativity, a blend is constructed by taking the existing commonalities among the input mental spaces—known as the generic space—into account, and by projecting their structure in a selective way. Since input spaces for interesting blends are often initially incompatible, a generalisation step is needed before they can be blended. In this paper, we apply this idea to blend input spaces specified in the description logic EL++ and propose an upward refinement operator for generalising EL++ concepts. We show how the generalisation operator is translated to Answer Set Programming (ASP) in order to implement a search process that finds possible generalisations of input concepts. We exemplify our approach in the domain of computer icons.COINVENT European Commission FP7 - 611553Peer reviewe