We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We start with different characterizations of answer sets in terms of totally colored dependency graphs that differ in graph-theoretical aspects. We then develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. In this way, we obtain an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Furthermore, we distinguish operations corresponding to Fitting's operator as well as to well-founded semantics.
Recently, strong equivalence for Answer Set Programming has been studied intensively, and was shown to be beneficial for modular programming and automated optimization. In this paper we define the novel notion of strong order equivalence for logic programs with preferences (ordered logic programs). Based on this definition we give, for several semantics for preference handling, necessary and sufficient conditions for programs to be strongly order equivalent. These results allow us also to associate a so-called SOE structure to each ordered logic program, such that two ordered logic programs are strongly order equivalent if and only if their SOE structures coincide. We also present the relationships among the studied semantics with respect to strong order equivalence, which differs considerably from their relationships with respect to preferred answer sets. Furthermore, we study the computational complexity of several reasoning tasks associated to strong order equivalence. Finally, based on the obtained results, we present -for the first timesimplification methods for ordered logic programs.
Mathematics Subject Classifications (2000)68T27 路 68T30 路 68T15
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