Strong Equivalence Made Easy: Nested Expressions and Weight Constraints

Strong Equivalence Made Easy: Nested Expressions and Weight Constraints

Strong Equivalence Made Easy: Nested Expressions and Weight Constraints

Strong equivalence made easy: nested expressions and weight constraints

Logic programs P and Q are strongly equivalent if, given any 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. Lifschitz, Pearce and Valverde showed that Heyting’s logic of here-an...

Alternative characterizations for strong equivalence of logic programs

In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a recent work by Lifschitz, Pearce and Valverde, strong equivalence can be simply reduced to equivalence in the logic of Here-and-There (HT). In this paper we pro...

Weight constraints as nested expressions

We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemelä and Simons, uses weight constraints. We show that there is a simple, modular translation from the language of weight constraints into the language of nested exp...