A Common View on Strong, Uniform, and Other Notions of Equivalence in Answer-Set Programming

Logic programming under the answer-set semantics nowadays deals with numerous different notions of equivalence between programs. This is due to the fact that equivalence for substitution (known as strong equivalence), which holds between programs P and Q iff P can faithfully be replaced by Q within any context R, is a different concept than ordinary equivalence between P and Q, which holds if P and Q have the same answer sets. Notions inbetween strong and ordinary equivalence have therefore been obtained by either restricting the syntactic structure of R or bounding the set of atoms allowed to occur in R (relativized equivalence). For the former approach, however, it turned out that any “reasonable” syntactic restriction to R either coincides with strong equivalence or collapses to uniform equivalence where R ranges over arbitrary sets of facts. In this paper, we propose a parameterization for equivalence notions which takes care of both such kinds of restrictions simultaneously by...

• Type: Conference
• Year: 2007
• Where: LPNMR
• Authors: Stefan Woltran
• Keywords: Equivalence Notions, LPNMR 2007, Ordinary Equivalence, Strong Equivalence