Abstract
Open answer set programming (OASP) solves the lack of modularity in closed world answer set programming by allowing for the grounding of logic programs with an arbitrary non-empty countable superset of the program’s constants. However, OASP is, in general, undecidable: the undecidable domino problem can be reduced to it. In order to regain decidability, we restrict the shape of logic programs, yielding conceptual logic programs (CoLPs). CoLPs are logic programs with unary and binary predicates (possibly inverted) where rules have a tree shape. Decidability of satisfiability checking of predicates w.r.t. CoLPs is shown by a reduction to non-emptiness checking of two-way alternating tree automata. We illustrate the expressiveness of CoLPs by simulating the description logic \(\mathcal{SHIQ}\). CoLPs thus integrate, in one unifying framework, the best of both the logic programming paradigm (a flexible rule-based representation and nonmonotonicity by means of negation as failure) and the description logics paradigm (decidable open domain reasoning).
Similar content being viewed by others
References
Alsaç, G., Baral, C.: Reasoning in description logics using declarative logic progamming. Technical Report, Arizona State University, Phoenix, Arizona (2002)
Andréka, H., Németi, I., Van Benthem, J.: Modal languages and bounded fragments of predicate logic. J. Philos. Logic 27(3), 217–274 (1998)
Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.: The Description Logic Handbook. Cambridge University Press, UK (2003)
Baader, F., Sattler, U.: Tableau algorithms for description logics. In: Proc of Tableaux 2000, vol. 1847 of LNAI, pp. 1–18. Springer, Berlin Heidelberg New York (2000)
Bechhofer, S., Goble, C., Horrocks, I.: DAML+OIL is not Enough. In: Proc of SWWS’01, pp. 151–159. CEUR, Stanford, California (2001)
Bechhofer, S., van Harmelen, F., Hendler, J., Horrocks, I., McGuinness, D.L., Patel-Schneider, P.F., Stein, L.A.:(OWL) Web Ontology Language Reference, Stanford University, California (2004)
Berners-Lee, T., Hendler, J., Lassila, O.: The semantic web. Sci. Am. 34–43 (May 2001)
Bonatti, P.A.: Reasoning with infinite stable models. Artif. Intell. 156, 75–111 (2004)
Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Perspectives of Mathematical Logic. Springer, Berlin Heidelberg New York (1997)
Bry, F., Schaffert, S.: An entailment relation for reasoning on the web. In: Proc of RuleML, LNCS, pp. 17–34. Springer, Berlin Heidelberg New York (2003)
Calvanese, D., De Giacomo, G., Lenzerini, M.: 2ATAs make DLs easy. In: Proc of the 2002 Description Logic Workshops (DL’02). Toulouse, France (2002)
Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and expressive power of logic programming. ACM Comput. Surv. 33(3), 374–425 (2001)
Donini, F., Lenzerini, M., Nardi, D., Schaerf, A.: AL-log: Integrating datalog and description logics. J. Intell. Syst. 10, 227–252 (1998)
Eiter, T., Ianni, G., Schindlauer, R., Tompits, H.: Nonmonotonic description logic programs: implemenation and experiments. In: Proc. of LPAR 2004, 3452 in LNAI, pp. 511–527. Springer, Berlin Heidelberg New York (2005)
Eiter, T., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with DLs for the semantic web. In: Proc. of KR 2004, pp. 141–151. Morgan Kaufmann, San Mateo, California (2004)
Fensel, D., Horrocks, I., van Harmelen, F., Decker, S., Erdmann, M., Klein, M.: OIL in a Nutshell. In: Proc. of EKAW 2000, LNAI. Springer, Berlin Heidelberg New York (2000)
Fensel, D., van Harmelen, F., Horrocks, I., McGuinness, D., Patel-Schneider, P.F.: OIL: An ontology infrastructure for the semantic web. IEEE Intell. Syst. 16(2), 38–45 (2001)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proc. of ICLP 1988, pp. 1070–1080. MIT, Cambridge, Massachusetts (1988)
Gelfond, M., Przymusinska, H.: Reasoning in open domains. In: Logic Programming and Non-Monotonic Reasoning, pp. 397–413. MIT, Cambridge, Massachusetts (1993)
Grosof, B., Horrocks, I., Volz, R., Decker, S.: Description logic programs: combining logic programs with description logic. In: Proc. of Twelfth International World Wide Web Conference (WWW 2003), pp. 48–57. ACM, Budapest, Hungary (2003)
Halpin, T.: Information Modeling and Relational Databases. Morgan Kaufmann, San Mateo, California (2001)
Horrocks, I., Patel-Schneider, P.F.: A proposal for an OWL rules language. Proc. of WWW 2004. ACM, New York (2004)
Horrocks, I., Sattler, U.: A description logic with transitive and converse roles and role hierarchies. LTCS-Report 98–05 (1998)
Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Proc. of LPAR’99, LNCS, pp. 161–180. Springer, Berlin Heidelberg New York (1999)
Horrocks, I., Schneider, P.F., Boley, H., Tabet, S., Grosof, B., Dean, M.: SWRL: A Semantic Web Rule Language Combining OWL and RuleML, (May 2004)
Hustadt, U., Motik, B., Sattler, U.: Reducing \(\mathcal{SHIQ}^{-}\) description logic to disjunctive datalog programs. FZI-Report 1-8-11/03 (2003)
Jarrar, M., Meersman, R.: Formal ontology engineering in the DOGMA approach. Proc. of CoopIS/DOA/ODBASE, vol. 2519 of LNCS, pp. 1238–1254. Springer, Berlin Heidelberg New York (2002)
Levy, A.Y., Rousset, M.: CARIN: A representation language combining horn rules and description logics. In: Proc. of ECAI’96, pp. 323–327, Budapest, Hungary (1996)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Trans. Comput. Syst. 2(4), 526–541 (2001)
Lutz, C., Sattler, U.: Mary likes all cats. In: Baader, F., Sattler, U. (eds.) Proc of DL 2000, number 33 in CEUR-WS, pp. 213–226, Aachen, Germany (2000)
Motik, B., Sattler, U., Studer, R.: Query answering for OWL-DL with rules. In: Proc of ISWC 2004, number 3298 in LNCS, pp. 549–563. Springer, Berlin Heidelberg New York (2004)
Motik, B., Volz, R., Maedche, A.: Optimizing query answering in description logics using disjunctive deductive databases. In: Proc. of KRDB’03, pp. 39–50, Humberg, Germany (2003)
Rector, A.L., Wroe, C., Rogers, J., Roberts, A.: Untangling taxonomies and relationships: personal and practical problems in loosely coupled development of large ontologies. In: Proc of K-CAP 2001, pp. 139–146. ACM, USA (2001)
Rosati, R.: Towards expressive KR systems integrating datalog and description logics: preliminary report. In: Proc. of DL’99, pp. 160–164. Linkping, Sweden (1999)
Rosati, R.: On the decidability and complexity of integrating ontologies and rules. J. Web. Sem. 3(1), pp. 41–60 (2005)
The Rule Markup Initiative. http://www.ruleml.org
Schlipf, J.: Some remarks on computability and open domain semantics. In Proc. of the Workshop on Structural Complexity and Recursion-Theoretic Methods in Logic Programming, Washington, District of Columbia (1993)
Swift, T.: Deduction in ontologies via answer set programming. In: Lifschitz, V., Niemelä, I. (eds.) Proc. of LPNMR 2004, vol. 2923 of LNCS, pp. 275–288. Springer, Berlin Heidelberg New York (2004)
Tobies S.: Complexity results and practical algorithms for logics in knowledge representation. PhD thesis, RWTH-Aachen, Germany (2001)
Uschold, M., Grüninger, M.: Ontologies: Principles, methods, and applications. Knowl. Eng. Rev. 11(2), 93–155 (1996)
Van Belleghem, K., Denecker, M., De Schreye, D.: A strong correspondence between DLs and open logic programming. In: Proc. of ICLP 1997, pp. 346–360. MIT, Cambridge, Massachusetts (1997)
van Emden, M.H., Kowalski, R.A.: The semantics of predicate logic as a programming language. J. ACM 23(4), 733–742 (1976)
Van Gelder, A., Schlipf, J.: Commonsense axiomatizations for logic programs. J. Log. Program. 17, 161–195 (1993)
Vardi, M.Y.: Why is modal logic so robustly decidable? Technical Report TR97-274, Rice University, Houston, Texas, April 12 (1997)
Vardi, M.Y.: Reasoning about the past with two-way automata. In: Proc. of ICALP’98, pp. 628–641. Springer, Berlin Heidelberg New York (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heymans, S., Van Nieuwenborgh, D. & Vermeir, D. Conceptual logic programs. Ann Math Artif Intell 47, 103–137 (2006). https://doi.org/10.1007/s10472-006-9030-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-006-9030-5