hex-Programs with Existential Quantification

HEX-programs extend ASP by external sources. In this paper, we present domain-specific existential quantifiers on top of HEX-programs, i.e., ASP programs with external access which may introduce new values that also show up in the answer sets. Pure logical existential quantification corresponds to a specific instance of our approach. Programs with existential quantifiers may have infinite groundings in general, but for specific reasoning tasks a finite subset of the grounding can suffice. We introduce a generalized grounding algorithm for such problems, which exploits domain-specific termination criteria in order to generate a finite grounding for bounded model generation. As an application we consider query answering over existential rules. In contrast to other approaches, several extensions can be naturally integrated into our approach. We further show how terms with function symbols can be handled by HEX-programs, which in fact can be seen as a specific form of existential quantification.