A "Conservative" Approach to Extending Answer Set Programming with Non-Herbrand Functions

In this paper we propose an extension of Answer Set Programming (ASP) by non-Herbrand functions, i.e. functions over non-Herbrand domains. Introducing support for such functions allows for an economic and natural representation of certain kinds of knowledge that are comparatively cumbersome to represent in ASP. The key difference between our approach and other techniques for the support of non-Herbrand functions is that our extension is more "conservative" from a knowledge representation perspective. In fact, we purposefully designed the new language so that (1) the representation of relations is fully retained; (2) the representation of knowledge using non-Herbrand functions follows in a natural way from the typical ASP strategies; (3) the semantics is an extension of the the semantics of ASP from [9], allowing for a comparatively simple incorporation of various extensions of ASP such as weak constraints, probabilistic constructs and consistency-restoring rules.

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