Equivalence Between Answer-Set Programs Under (Partially) Fixed Input
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Answer Set Programming (ASP) has become an increasingly popular formalism for declarative problem solving. Among the huge body of theoretical results, investigations of different equivalence notions between logic programs play a fundamental role for understanding modularity and optimization. While strong equivalence between two programs holds if they can be faithfully replaced by each other in any context (facts and rules), uniform equivalence amounts to equivalent behavior of programs under any set of facts. Both notions (as well as several variants thereof) have been extensively studied. However, the somewhat reverse notion of equivalence which holds if two programs are equivalent under the addition of any set of proper rules (i.e., all rules except facts) has not been investigated yet. In this paper, we close this gap and give a thorough study of this notion, which we call rule equivalence (RE), and its parameterized version where we allow facts over a given restricted alphabet to appear in the context. RE is thus a relationship between two programs whose input is (partially) fixed but where additional proper rules might still be added. Such a notion might be helpful in debugging of programs. We give full characterization results and a complexity analysis for the propositional case of RE. Moreover, we show that RE is decidable in the non-ground case.
KeywordsUniform Equivalence Strong Equivalence Equivalence Rules (RE) Answer Set Equivalence Notions
This work was supported by the Austrian Science Fund (FWF) projects P25607 and Y698.
- 5.Eiter, T., Fink, M., Tompits, H., Woltran, S.: Strong and uniform equivalence in answer-set programming: characterizations and complexity results for the non-ground case. In: Proceedings of the 20th National Conference on Artificial Intelligence (AAAI 2005), pp. 695–700. AAAI Press (2005)Google Scholar
- 13.Oikarinen, E., Janhunen, T.: Modular equivalence for normal logic programs. In: Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), pp. 412–416. IOS Press (2006)Google Scholar
- 15.Sagiv, Y.: Optimizing datalog programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 659–698. Morgan Kaufmann, USA (1988)Google Scholar