Discovering Classes of Strongly Equivalent Logic Programs

In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules

Strong Equivalence for Logic Programs and Default Theories (Made Easy)

Logic programs P and Q are strongly equivalent if, given any logic program R, programs P R and Q R are equivalent (that is, have the same answer sets). Strong equivalence is convenient for the study of equivalent transformations of logic programs: one can prove that a local change is correct without considering the whole program. Recently, Lifschitz, Pearce and Valverde showed that Heyting's logic of here-and-there can be used to characterize strong equivalence of logic programs. This paper offers a more direct characterization, and extends it to default logic. In their paper, Lifschitz, Pearce and Valverde study a very general form of logic programs, called "nested" programs. For our study of strong equivalence of default theories, we find it convenient to introduce a corresponding "nested" version of default logic, which generalizes Reiter's default logic