Abstract
Disjunctive logic programming under the answer set semantics (DLP, ASP) has been acknowledged as a versatile formalism for knowledge representation and reasoning during the last decade. Lifschitz, Tang, and Turner have introduced an extended language of DLP, called Nested Logic Programming (NLP), in 1999 [1]. It often allows for more concise representations by permitting a richer syntax in rule heads and bodies. However, that language is propositional and thus does not allow for variables, one of the strengths of DLP.
In this paper, we introduce a language similar to NLP, called Normal Form Nested (NPN) programs, which does allow for variables, and present the syntax and semantics. With the presence of variables, domain independence is no longer guaranteed. We study this issue in depth and define the class of safe NPN programs, which are guaranteed to be domain independent. Moreover, we show that for NPN programs which are also NLPs, our semantics coincides with the one of [1]; while keeping the standard meaning of answer sets on DLP programs with variables. Finally, we provide an algorithm which translates NPN programs into DLP programs, and does so in an efficient way, allowing for the effective implementation of the NPN language on top of existing DLP systems.
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References
Lifschitz, V., Tang, L.R., Turner, H.: Nested Expressions in Logic Programs. AMAI 25(3–4), 369–389 (1999)
Przymusinski, T.C.: Stable Semantics for Disjunctive Programs. NGC 9, 401–424 (1991)
Gelfond, M., Lifschitz, V.: Classical Negation in Logic Programs and Disjunctive Databases. NGC 9, 365–385 (1991)
Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)
Pearce, D., Sarsakov, V., Schaub, T., Tompits, H., Woltran, S.: A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 405–420. Springer, Heidelberg (2002)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV System for Knowledge Representation and Reasoning. ACM TOCL 7(3), 499–562 (2006)
Janhunen, T., Niemelä, I.: Gnt - a solver for disjunctive logic programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 331–335. Springer, Heidelberg (2003)
Lierler, Y.: Disjunctive Answer Set Programming via Satisfiability. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 447–451. Springer, Heidelberg (2005)
Bertossi, L.E.: Consistent query answering in databases. SIGMOD Record 35(2), 68–76 (2006)
Stewart, I.A.: Complete problems involving boolean labelled structures and projection transactions. Journal of Logic and Computation 1(6), 861–882 (1991)
Eiter, T., Gottlob, G., Mannila, H.: Disjunctive Datalog. ACM TODS 22(3), 364–418 (1997)
Faber, W., Leone, N., Pfeifer, G.: Recursive aggregates in disjunctive logic programs: Semantics and complexity. In: Alferes, J.J., Leite, J.A. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 200–212. Springer, Heidelberg (2004)
Plaisted, D.A., Greenbaum, S.: A Structure-Preserving Clause Form Translation. Journal of Symbolic Computation 2(3), 293–304 (1986)
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Bria, A., Faber, W., Leone, N. (2008). Normal Form Nested Programs. In: Hölldobler, S., Lutz, C., Wansing, H. (eds) Logics in Artificial Intelligence. JELIA 2008. Lecture Notes in Computer Science(), vol 5293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87803-2_8
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DOI: https://doi.org/10.1007/978-3-540-87803-2_8
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