Graphs and Colorings for Answer Set Programming with Preferences

Issue title: The 1st International Workshop on Knowledge Representation and Approximate Reasoning (KR&AR)

Article type: Research Article

Authors: Konczak, Kathrin | Schaub, Torsten | Linke, Thomas

Affiliations: Institut für Informatik, Universität Potsdam, Postfach 90 03 27, D-14439 Potsdam, Germany

Abstract: The integration of preferences into answer set programming constitutes an important practical device for distinguishing certain preferred answer sets from non–preferred ones. To this end, we elaborate upon rule dependency graphs and their colorings for characterizing different preference handling strategies found in the literature. We start from a characterization of (three types of) preferred answer sets in terms of totally colored dependency graphs. In particular, we demonstrate that this approach allows us to capture all three approaches to preferences in a uniform setting by means of the concept of a height function. In turn, we exemplarily develop an operational characterization of preferred answer sets in terms of operators on partial colorings for one particular strategy. In analogy to the notion of a derivation in proof theory, our operational characterization is expressed as a (non–deterministically formed) sequence of colorings, gradually turning an uncolored graph into a totally colored one.

Journal: Fundamenta Informaticae, vol. 57, no. 2-4, pp. 393-421, 2003