Abstract
The support for function symbols in logic programming under answer set semantics allows to overcome some modeling limitations of traditional Answer Set Programming (ASP) systems, such as the inability of handling infinite domains. On the other hand, admitting function symbols in ASP makes inference undecidable in the general case. Lately, the research community is focusing on finding proper subclasses for which decidability of inference is guaranteed. The two major proposals, so far, are finitary programs and finitely-ground programs. These two proposals are somehow complementary: indeed, the former is conceived to allow decidable querying (by means of a top-down evaluation strategy), while the latter supports the computability of answer-sets (by means of a bottom-up evaluation strategy). One of the main advantages of finitely-ground programs is that they can be ”directly” evaluated by current ASP systems, which are based on a bottom-up computational model. However, there are also some interesting programs which are suitable for top-down query evaluation; but do not fall in the class of finitely-ground programs.
In this paper, we focus on disjunctive finitely-recursive positive (DFRP) programs. We present a proper adaptation of the magic-sets technique for DFRP programs, which ensures query equivalence under both brave and cautious reasoning. We show that, if the input program is DFRP, then its magic-set rewriting is guaranteed to be finitely ground. Thus, reasoning on DFRP programs turns out to be decidable, and we provide an effective method for its computation on the ASP system DLV.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. CUP (2003)
Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: ICLP/SLP 1988, pp. 1070–1080. MIT Press, Cambridge (1988)
Gelfond, M., Lifschitz, V.: Classical Negation in Logic Programs and Disjunctive Databases. NGC 9, 365–385 (1991)
Lifschitz, V.: Answer Set Planning. In: ICLP 1999, pp. 23–37 (1999)
Marek, V.W., Truszczyński, M.: Stable Models and an Alternative Logic Programming Paradigm. In: The Logic Programming Paradigm – A 25-Year Perspective, pp. 375–398 (1999)
Syrjänen, T.: Omega-restricted logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, p. 267. Springer, Heidelberg (2001)
Bonatti, P.A.: Reasoning with infinite stable models II: Disjunctive programs. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 333–346. Springer, Heidelberg (2002)
Bonatti, P.A.: Reasoning with infinite stable models. AI 156(1), 75–111 (2004)
Simkus, M., Eiter, T.: FDNC: Decidable Non-monotonic Disjunctive Logic Programs with Function Symbols. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 514–530. Springer, Heidelberg (2007)
Lin, F., Wang, Y.: Answer Set Programming with Functions. In: KR 2008, Sydney, Australia, pp. 454–465. AAAI Press, Menlo Park (2008)
Cabalar, P.: Partial Functions and Equality in Answer Set Programming. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 392–406. Springer, Heidelberg (2008)
Calimeri, F., Cozza, S., Ianni, G., Leone, N.: Computable Functions in ASP: Theory and Implementation. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 407–424. Springer, Heidelberg (2008)
Baselice, S., Bonatti, P.A., Criscuolo, G.: On Finitely Recursive Programs. Tech. Report 0901.2850v1, arXiv.org (2009); To appear in TPLP (TPLP)
Bonatti, P.A.: Erratum to: Reasoning with infinite stable models. AI 172(15), 1833–1835 (2008)
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)
Calimeri, F., Cozza, S., Ianni, G., Leone, N.: DLV-Complex, homepage (since 2008), http://www.mat.unical.it/dlv-complex
Marano, M., Ianni, G., Ricca, F.: A Magic Set Implementation for Disjunctive Logic Programming with Function Symbols. Submitted to CILC 2009 (2009)
Bancilhon, F., Maier, D., Sagiv, Y., Ullman, J.D.: Magic Sets and Other Strange Ways to Implement Logic Programs. In: PODS 1986, Cambridge, Massachusetts, pp. 1–15 (1986)
Ullman, J.D.: Principles of Database and Knowledge Base Systems, vol. 2. Computer Science Press (1989)
Beeri, C., Ramakrishnan, R.: On the Power of Magic. In: PODS 1987, pp. 269–284. ACM, New York (1987)
Cumbo, C., Faber, W., Greco, G., Leone, N.: Enhancing the magic-set method for disjunctive datalog programs. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 371–385. Springer, Heidelberg (2004)
Van Gelder, A., Ross, K.A., Schlipf, J.S.: The Well-Founded Semantics for General Logic Programs. J. ACM 38(3), 620–650 (1991)
Lifschitz, V., Turner, H.: Splitting a Logic Program. In: ICLP 1994, pp. 23–37. MIT Press, Cambridge (1994)
Naqvi, S., Tsur, S.: A logical language for data and knowledge bases. CS Press, NY (1989)
Schreye, D.D., Decorte, S.: Termination of Logic Programs: The Never-Ending Story. JLP 19/20, 199–260 (1994)
Bossi, A., Cocco, N., Fabris, M.: Norms on Terms and their use in Proving Universal Termination of a Logic Program. Theoretical Computer Science 124(2), 297–328 (1994)
Bruynooghe, M., Codish, M., Gallagher, J.P., Genaim, S., Vanhoof, W.: Termination analysis of logic programs through combination of type-based norms. ACM TOPLAS 29(2), 10 (2007)
Behrend, A.: Soft stratification for magic set based query evaluation in deductive databases. In: PODS 2003, San Diego, CA, USA, pp. 102–110 (2003)
Faber, W., Greco, G., Leone, N.: Magic Sets and their Application to Data Integration. JCSS 73(4), 584–609 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Calimeri, F., Cozza, S., Ianni, G., Leone, N. (2009). Magic Sets for the Bottom-Up Evaluation of Finitely Recursive Programs. In: Erdem, E., Lin, F., Schaub, T. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2009. Lecture Notes in Computer Science(), vol 5753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04238-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-04238-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04237-9
Online ISBN: 978-3-642-04238-6
eBook Packages: Computer ScienceComputer Science (R0)