Abstract
A general framework is proposed for integration of rules and external first-order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program consists of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized in description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers (such as ontology reasoners). Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics and for completeness of the operational semantics are given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Antoniou G, Damásio CV, Grosof B, Horrocks I, Kifer M, Małuszyński J, Patel-Schneider PF (2005) Combining rules and ontologies. a survey. FP6 NoE REWERSE, Deliverable I3-D3, Available at. http://rewerse.net/deliverables/m12/i3-d3.pdf
Apt KR (1997) From logic programming to prolog, International series in computer science. Prentice-Hall, Englewood Cliffs
Apt KR, Bol RN (1994) Logic programming and negation: a survey. J Log Program 19/20: 9–71
Baader, F, Calvanese, D, McGuiness, D, Nardi, D, Patel-Schneider, P (eds) (2003) The description logic handbook. Cambridge University Press, Cambridge
Baral C, Gelfond M (1994) Logic programming and knowledge representation. J Log Program 19/20: 73–148
Clark KL (1978) Negation as failure. In: Gallaire H, Minker J (eds) Logic and databases. Plenum Press, New York, pp 293–322
de Bruijn J, Eiter T, Tompits H (2008) Embedding approaches to combining rules and ontologies into autoepistemic logic. In: Brewka G, Lang J (eds) KR. AAAI Press, pp 485–495
de Bruijn J, Pearce D, Polleres A, Valverde A (2007) Quantified equilibrium logic and hybrid rules. In: Marchiori et al. [29] pp 58–72
Dix J, Stolzenburg F (1998) A framework to incorporate non-monotonic reasoning into constraint logic programming. J Log Program 37(1–3): 47–76
Donini F, Lenzerini M, Nardi D, Schaerf A (1998) AL-Log: integrating datalog and description logics. Int Inf Syst 10(3): 227–252
Drabent W (1993) SLS-resolution without floundering. In: Pereira LM, Nerode A (eds) Proceedings of 2nd international workshop on logic programming and non-monotonic reasoning. MIT Press, pp 82–98
Drabent W (1995) What is failure? An approach to constructive negation. Acta Inform 32(1): 27–59
Drabent W, Eiter T, Ianni G, Krennwallner T, Lukasiewicz T, Małuszyński J (2009) Hybrid reasoning with rules and ontologies. In: Bry F, Małuszyński J (eds) Semantic techniques for the web. The REWERSE perspective, vol 5500 of lecture notes in computer science. Springer, pp 1–49
Drabent W, Henriksson J, Małuszyński J (2007a) HD-rules: a hybrid system interfacing prolog with DL-reasoners. In: Proceedings of the ICLP’07 workshop on applications of logic programming to the web, semantic web and semantic web services (ALPSWS2007), CEUR workshop proceedings, vol 287. http://www.ceur-ws.org/Vol-287. Updated version of (Drabent et al. [15])
Drabent W, Henriksson J, Małuszyński J (2007b) Hybrid reasoning with rules and constraints under well-founded semantics, In: Marchiori et al. [29] pp 348–357
Drabent W, Małuszyński J (2007) Well-founded semantics for hybrid rules. In: Marchiori et al. [29] pp 1–15
Eiter T, Ianni G, Schindlauer R, Tompits H (2006) Effective integration of declarative rules with external evaluations for semantic-web reasoning. In: Sure Y, Domingue J (eds) ESWC vol 4011 of lecture notes in computer science, Springer, pp 273–287
Eiter T, Lukasiewicz T, Schindlauer R, Tompits H (2004a) Combining answer set programming with description logics for the semantic web. In: Proceedings of the international conference of knowledge representation and reasoning (KR’04). http://citeseer.ist.psu.edu/eiter04combining.html
Eiter T, Lukasiewicz T, Schindlauer R, Tompits H (2004b) Well-founded semantics for description logic programs in the semantic web. In: Antoniou G, Boley H (eds) RuleML vol 3323 of lecture notes in computer science. Springer, pp 81–97
Fages F (1997) Constructive negation by pruning. J Log Program 32(2): 85–118
Ferrand G, Deransart P (1993) Proof method of partial correctness and weak completeness for normal logic programs. J Log Program 17(2/3&4): 265–278
Gelfond M, Lifschitz V (1988) The stable model semantics for logic programming. In: Kowalski RA, Bowen K (eds) Proceedings of the fifth international conference on logic programming. The MIT Press, Cambridge, Massachusetts, pp 1070–1080
Gruber TR (1995) Towards principles for the design of ontologies used for knowledge sharing. J Hum Comput Stud 43: 907–928
Horrocks I, Patel-Schneider PF (2004) A proposal for an OWL rules language. WWW ’04: Proceedings of the 13th international conference on World Wide Web. ACM, New York, NY, USA, pp 723–731
Kunen K (1987) Negation in logic programming. J Log Program 4(4): 289–308
Levy A, Rousset M-C (1998) Combining horn rules and description logics in carin. Artif Intell 104(1–2): 165–209
Lloyd JW (1987) Foundations of logic programming, second extended edn. Springer, Berlin
Małuszyński J (2009) Integration of rules and ontologies. In: Liu L, Özsu MT (eds) Encyclopedia of database systems. Springer US, pp 1546–1551
Marchiori M, Pan JZ, de Sainte Marie C (eds) (2007) Web reasoning and rule systems, first international conference, RR 2007, Innsbruck, Austria, June 7–8, 2007, Proceedings, vol 4524 of lecture notes in computer science, Springer
Marriott K, Stuckey PJ, Wallace M (2006) Constraint logic programming. Handbook of constraint programming. Elsevier, Amsterdam
Motik B, Rosati R (2007) A faithful integration of description logics with logic programming. In: Veloso MM (ed) IJCAI 2007, Proceedings of the 20th international joint conference on artificial intelligence. pp 477–482
Motik B, Sattler U, Studer R (2005) Query answering for OWL-DL with rules. J Web Sem 3(1): 41–60
Patel-Schneider PF, Hayes P, Horrocks I (2004) OWL web ontology language semantics and abstract syntax, W3C Recommendation. Available at. http://www.w3.org/TR/owl-semantics/
Przymusinski TC (1989) On the declarative and procedural semantics of logic programs. J Autom Reason 5: 167–205
Rosati R (2005) On the decidability and complexity of integrating ontologies and rules. J Web Semant 3: 61–73
Rosati R (2006) \({{\mathcal DL}}\) + log: tight integration of description logics and disjunctive datalog. In: Doherty P, Mylopoulos J, Welty CA (eds) KR. AAAI Press, Menlo Park, pp 68–78
Sagonas C, Swift T, Warren DS et al. (2007) The XSB system. Volume1: programmer’s manual. Available at. http://xsb.sourceforge.net
Shoenfield JR (1967) Mathematical logic. Addison-Wesley, Reading
Stuckey PJ (1995) Negation and constraint logic programming. Inf Comput 118(1): 12–33
van Gelder A, Ross KA, Schlipf JS (1988) Unfounded sets and well-founded semantics for general logic programs. Principles of database systems. ACM, pp 221–230
Acknowledgments
This research has been partially funded by the European Commission and by the Swiss Federal Office for Education and Science within the 6th Framework Programme project REWERSE number 506779(cf. http://rewerse.net).
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Drabent, W., Małuszyński, J. Hybrid rules with well-founded semantics. Knowl Inf Syst 25, 137–168 (2010). https://doi.org/10.1007/s10115-010-0300-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10115-010-0300-5