Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-24T08:52:32.505Z Has data issue: false hasContentIssue false
  • English
  • Français

Disjunctive ASP with functions: Decidable queries and effective computation*

Published online by Cambridge University Press:  09 July 2010

MARIO ALVIANO ,
WOLFGANG FABER  and
NICOLA LEONE
MARIO ALVIANO
Affiliation:
Department of Mathematics, University of Calabria, 87036 Rende (CS), Italy (e-mail: alviano@mat.unical.it, faber@mat.unical.it, leone@mat.unical.it)
WOLFGANG FABER
Affiliation:
Department of Mathematics, University of Calabria, 87036 Rende (CS), Italy (e-mail: alviano@mat.unical.it, faber@mat.unical.it, leone@mat.unical.it)
NICOLA LEONE
Affiliation:
Department of Mathematics, University of Calabria, 87036 Rende (CS), Italy (e-mail: alviano@mat.unical.it, faber@mat.unical.it, leone@mat.unical.it)
Get access Rights & Permissions [Opens in a new window]

Abstract

Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASPfs). We show that query answering in this setting is decidable, if the query is finitely recursive (ASPfsfr). Our proof yields also an effective method for query evaluation. It is done by extending the magic set technique to ASPfsfr. We show that the magic-set rewritten program is query equivalent to the original one (under both brave and cautious reasoning). Moreover, we prove that the rewritten program is also finitely ground, implying that it is decidable. Importantly, finitely ground programs are evaluable using existing ASP solvers, making the class of ASPfsfr queries usable in practice.

Keywords

answer set programmingdecidabilitymagic setsdisjunctive logic programs
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 10 , Special Issue 4-6: 26th International Conference on Logic Programming , July 2010 , pp. 497 - 512
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alviano, M., Faber, W., Greco, G., and Leone, N. 2009. Magic Sets for Disjunctive Datalog Programs. Technical Report 09/2009, Dipartimento di Matematica, Università della Calabria, Italy. http://www.wfaber.com/research/papers/TRMAT092009.pdf.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.CrossRefGoogle Scholar
Baselice, S., Bonatti, P. A., and Criscuolo, G. 2009. On finitely recursive programs. Theory and Practice of Logic Programming 9, 2, 213–238.Google Scholar
Beeri, C. and Ramakrishnan, R. 1991. On the power of magic. Journal of Logic Programming 10, 1–4, 255–259.Google Scholar
Bonatti, P. A. 2002. Reasoning with infinite stable models II: Disjunctive programs. In Proceedings of the 18th International Conference on Logic Programming (ICLP 2002). Lecture Notes in Computer Science, vol. 2401. Springer, 333–346.Google Scholar
Bonatti, P. A. 2004. Reasoning with infinite stable models. Artificial Intelligence 156, 1, 75–111.CrossRefGoogle Scholar
Bruynooghe, M., Codish, M., Gallagher, J. P., Genaim, S., and Vanhoof, W. 2007. Termination analysis of logic programs through combination of type-based norms. ACM Transactions on Programming Languages and Systems (TOPLAS) 29, 2, 10.Google Scholar
Cabalar, P. 2008. Partial Functions and Equality in Answer Set Programming. In Proceedings of the 24th International Conference on Logic Programming (ICLP 2008). Lecture Notes in Computer Science, vol. 5366. Springer, Udine, Italy, 392–406.Google Scholar
Calimeri, F., Cozza, S., Ianni, G., and Leone, N. 2008a. Computable Functions in ASP: Theory and implementation. In Proceedings of the 24th International Conference on Logic Programming (ICLP 2008). Lecture Notes in Computer Science, vol. 5366. Springer, Udine, Italy, 407–424.Google Scholar
Calimeri, F., Cozza, S., Ianni, G., and Leone, N. 2008b. DLV-Complex homepage. http://www.mat.unical.it/dlv-complex.Google Scholar
Calimeri, F., Cozza, S., Ianni, G., and Leone, N. 2009. Magic sets for the bottom-up evaluation of finitely recursive programs. In Logic Programming and Nonmonotonic Reasoning — 10th International Conference (LPNMR 2009), Erdem, E., Lin, F., and Schaub, T., Eds. Lecture Notes in Computer Science, vol. 5753. Springer, 71–86.CrossRefGoogle Scholar
Eiter, T. and Simkus, M. 2009. Bidirectional answer set programs with function symbols. In Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI-09), Boutilier, C., Ed. Springer, Pasadena, CA, 765–771.Google Scholar
Gebser, M., Schaub, T., and Thiele, S. 2007. Gringo: A new grounder for answer set programming. In Logic Programming and Nonmonotonic Reasoning—9th International Conference, LPNMR'07, Baral, C., Brewka, G., and Schlipf, J., Eds. Lecture Notes in Computer Science, vol. 4483. Springer, Tempe, Arizona, 266–271.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.CrossRefGoogle Scholar
Greco, S. 2003. Binding propagation techniques for the optimization of bound disjunctive queries. IEEE Transactions on Knowledge and Data Engineering 15, 2 (March/April), 368–385.CrossRefGoogle Scholar
Kemp, D. B., Srivastava, D., and Stuckey, P. J. 1995. Bottom-up evaluation and query optimization of well-founded models. Theoretical Computer Science 146, 145–184.CrossRefGoogle Scholar
Leone, N., Rullo, P., and Scarcello, F. 1997. Disjunctive stable models: Unfounded sets, fixpoint semantics and computation. Information and Computation 135, 2 (June), 69–112.Google Scholar
Lierler, Y. and Lifschitz, V. 2009. One more decidable class of finitely ground programs. In Proceedings of the 25th International Conference on Logic Programming (ICLP 2009). Lecture Notes in Computer Science, vol. 5649. Springer, Pasadena, CA, 489–493.Google Scholar
Lin, F. and Wang, Y. 2008. Answer set programming with functions. In Proceedings of Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR2008). AAAI Press, Sydney, Australia, 454–465.Google Scholar
Simkus, M. and Eiter, T. 2007. FDNC: Decidable non-monotonic disjunctive logic programs with function symbols. In Proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR2007). Lecture Notes in Computer Science, vol. 4790. Springer, 514–530.Google Scholar
Syrjänen, T. 2001. Omega-restricted logic programs. In Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning. Springer, Vienna, Austria, 267–279.Google Scholar
Tärnlund, S.-Å. 1977. Horn clause computability. BIT Numerical Mathematics 17, 2 (June), 215–226.Google Scholar
Ullman, J. D. 1989. Principles of Database and Knowledge Base Systems. Computer Science Press.Google Scholar