Abstract
In the ongoing discussion about combining rules and ontologies on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper, we show how Quantified Equilibrium Logic (QEL) can function as a unified framework which embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL, we relax the unique names assumption, which was present in earlier versions of QEL. Moreover, we show that this framework elegantly captures the existing modular approaches for hybrid knowledge bases in a unified way.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Baral C (2002) Knowledge representation, reasoning and declarative problem solving. Cambridge University Press, Cambridge
Cabalar P, Odintsov SP, Pearce D, Valverde A (2006) Analysing and extending well-founded and partial stable semantics using partial equilibrium logic. In: Proceedings of the 22nd international conference on logic programming (ICLP 2006), vol 4079 of lecture notes in computer science. Springer, Seattle, WA, USA, pp 346–360
de Bruijn J, Eiter T, Polleres A, Tompits H (2006) On representational issues about combinations of classical theories with nonmonotonic rules. In: Proceedings of the first international conference on knowledge science, Engineering and management (KSEM’06), number 4092 in lecture notes in computer science, Springer-Verlag, Guilin, China
de Bruijn J, Eiter T, Polleres A, Tompits H (2007) Embedding non-ground logic programs into autoepistemic logic for knowledge-base combination. In: Proceedings of the twentieth international joint conference on artificial intelligence (IJCAI-07), AAAI, Hyderabad, India, pp 304–309
de Bruijn J, Pearce D, Polleres A, Valverde A (2007) Quantified equilibrium logic and hybrid rules, In: First international conference on web reasoning and rule systems (RR2007), vol 4524 of lecture notes in computer science, Springer, Innsbruck, Austria, pp 58–72
de Bruijn J, Eiter T, Tompits H (2008) Embedding approaches to combining rules and ontologies into autoepistemic logic. In: Proceedings of the 11th international conference on principles of knowledge representation and reasoning (KR2008), AAAI, Sydney, Australia, pp 485–495
Drabent W, Henriksson J, Maluszynski J (2007) Hybrid reasoning with rules and constraints under well-founded semantics, In: First international conference on web reasoning and rule systems (RR2007), vol 4524 of lecture notes in computer science, Springer, Innsbruck, Austria, pp 348–357
Eiter T, Fink M, Tompits H, Woltran S (2005) Strong and uniform equivalence in answer-set programming: characterizations and complexity results for the non-ground case. In: Proceedings of the twentieth national conference on artificial intelligence and the seventeenth innovative applications of artificial intelligence conference, pp 695–700
Eiter T, Ianni G, Schindlauer R, Tompits H (2005) A uniform integration of higher-order reasoning and external evaluations in answer-set programming. In: IJCAI 2005, pp 90–96
Eiter T, Lukasiewicz T, Schindlauer R, Tompits H (2004) Combining answer set programming with description logics for the semantic web. In: Proceedings of the ninth international conference on principles of knowledge representation and reasoning (KR’04)
Ensan F, Du W (2009) A knowledge encapsulation approach to ontology modularization. Knowledge and Information Systems Online First, to appear
Ferraris P, Lee J, Lifschitz V (2007) A new perspective on stable models. In: Proceedings of the twentieth international joint conference on artificial intelligence (IJCAI-07), AAAI, Hyderabad, India, pp 372–379
Ghilardi S, Lutz C, Wolter F (2006) Did I damage my ontology: a case for conservative extensions of description logics. In: Proceedings of the tenth international conference on principles of knowledge representation and reasoning (KR’06), pp 187–197
Heymans S (2006) Decidable open answer set programming, PhD thesis, Theoretical Computer Science Lab (TINF). Department of Computer Science, Vrije Universiteit Brussel, Brussels, Belgium
Heymans S, Nieuwenborgh DV, Vermeir D (2005) Guarded open answer set programming. In: 8th International conference on logic programming and non monotonic reasoning (LPNMR 2005), volume 3662 in ‘LNAI’, Springer, pp 92–104
Heymans S, Predoiu L, Feier C, de Bruijn J, van Nieuwenborgh D (2006) G-hybrid knowledge bases. In: Workshop on applications of logic programming in the semantic web and semantic web services (ALPSWS 2006)
Jing Y, Jeong D, Baik D-K (2009) SPARQL graph pattern rewriting for OWL-DL inference queries. Knowl Inf Syst 20: 243–262
Knorr M, Alferes J, Hitzler P (2008) A coherent well-founded model for hybrid mknf knowledge bases. In: 18th European conference on artificial intelligence (ECAI2008). Volume 178 in ‘Frontiers in artificial intelligence and applications’, IOS Press, pp 99–103
Lifschitz V, Pearce D, Valverde A (2001) Strongly equivalent logic programs. ACM Trans Comput Log 2(4): 526–541
Lifschitz V, Pearce D, Valverde A (2007) A characterization of strong equivalence for logic programs with variables. In: 9th International conference on logic programming and nonmonotonic reasoning (LPNMR), Vol. 4483 of lecture notes in computer science, Springer, Tempe, AZ, USA, pp 188–200
Lifschitz V, Woo T (1992) Answer sets in general nonmonotonic reasoning (preliminary report). In: Nebel B, Rich C, Swartout W (eds) ‘KR’92. Principles of knowledge representation and reasoning: proceedings of the third international conference, Morgan Kaufmann, San Mateo, California, pp 603–614
Lin F (2002) Reducing strong equivalence of logic programs to entailment in classical propositional logic. In: Proceedings of the eights international conference on principles of knowledge representation and reasoning (KR’02), pp 170–176
Motik B, Rosati R (2007) A faithful integration of description logics with logic programming. In: Proceedings of the twentieth international joint conference on artificial intelligence (IJCAI-07), AAAI, Hyderabad, India, pp 477–482
Pearce D (1997) A new logical characterization of stable models and answer sets. In: Proceedings of NMELP 96, vol 1216 of lecture notes in computer science, Springer, pp 57–70
Pearce D (2006) ‘Equilibrium logic’. Ann Math Artif Intell 47: 3–41
Pearce D, Valverde A (2005) A first-order nonmonotonic extension of constructive logic. Studia Logica 80: 321–346
Pearce D, Valverde A, (2006) Quantfied equilibrium logic, Technical report, Universidad Rey Juan Carlos, (in press)
Polleres A (2007) From SPARQL to rules (and back), in ‘WWW 2007’, pp 787–796
Rosati R (2005) On the decidability and complexity of integrating ontologies and rules. J Web Semant 3(1): 61–73
Rosati R (2005b) Semantic and computational advantages of the safe integration of ontologies and rules. In: Proceedings of the third international workshop on principles and practice of semantic web reasoning (PPSWR 2005), vol 3703 of lecture notes in computer science, Springer, pp 50–64
Rosati R (2006) \({\mathcal{DL}+log}\): tight integration of description logics and disjunctive datalog. In: Proceedings of the tenth international conference on principles of knowledge representation and reasoning (KR’06), pp 68–78
van Dalen D (1983) Logic and structure. Springer, Berlin
Wang K, Billington D, Blee J, Antoniou G (2004) Combining description logic and defeasible logic for the semantic web. In: Proceedings of the third international workshop rules and rule markup languages for the semantic web (RuleML 2004), vol 3323 of lecture notes in computer science, Springer, pp 170–181
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
de Bruijn, J., Pearce, D., Polleres, A. et al. A semantical framework for hybrid knowledge bases. Knowl Inf Syst 25, 81–104 (2010). https://doi.org/10.1007/s10115-010-0294-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10115-010-0294-z