AL-Log

[Donini et al., 1998]

Jos de BruijnDigital Enterprise Research Institute

jos.de-bruijn@{deri.at, deri.ie, uibk.ac.at}

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

22004-06-23

Agenda

• Motivation• The structural subsystem: ALC• The relational subsystem• AL-log• Hybrid Deduction• Conclusion

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

32004-06-23

Motivation

• Provide hybrid reasoning with representational adequacy and deductive power

• Specification of constraint in Datalog clauses

• Reasoning with incomplete information

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

42004-06-23

The Description Logic ALC

• Structural Subsystem of AL-log

• Adheres to UNA, i.e.

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

52004-06-23

Relational subsystem

• Constrained Datalog program• A constrained clause is a clause with a set of

restrictions on its variables and constants, expressed using the language ALC.

• In fact, it is a datalog clause with concepts occurring as unary predicates.

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

62004-06-23

AL-log Knowledge Bases

• An AL-log knowledge base K = (Σ,Π)– Σ is an ALC knowledge base– Π is a constrained datalog program

• An acceptable knowledge base must satisfy the conditions:– Predicate symbols in Π is disjoint from the

concept and role symbols in Σ– The alphabet of constants in Π coincides with

the alphabet of individuals in Σ– In Π, each variable occurring in a DL

predicate, must also occur in a non-DL predicate

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

72004-06-23

AL-log semantics

• An interpretation J for K = (Σ,Π) is defined as the union of an interpretation I for Σ and a Herbrand interpretation H for ΠD, where ΠD is obtained from Π by deleting the DL predicates

• J = (I,H) is a model of K if I is a model of Σ and for each ground clause in Π, either one of the DL predicates is not satisfied by J or the non-DL part of the clause is satisfied by J

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

82004-06-23

Example

• Graph 3-colorability (NP-complete problem)

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92004-06-23

Hybrid Deduction

• Constrained SLD-resolution for K = (Σ,Π)

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102004-06-23

Hybrid Deduction cont’d

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112004-06-23

jos.de-bruijn@{deri.ie, deri.at, uibk.ac.at}

122004-06-23

Conclusion

• AL-log does not allow relational subsystem to deduce knowledge about the structural subsystem

• No roles allowed in rule bodies• Results of DL satisfiability check used for

checking constraints in query answering• Defines an interface between DL and datalog by

allowing datalog program to “query” DL KB

• AL-log extended with roles in rule body by [Rosatti, 1999]

• [Eiter et al., 2004] extend the approach for more expressive DLs and more expressive LP language

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132004-06-23

References• [Donini et al., 1998] Donini, F. M., Lenzerini, M., Nardi, D., and

Schaerf, A. (1998). Al-log: integrating datalog and description logics. Journal of Intelligent Information Systems, 10:227-252.

• [Eiter et al., 2004] Thomas Eiter, Thomas Lukasiewicz, Roman Schindlauer, and Hans Tompits. Combining answer set programming with description logics for the semantic web. In Proc. of the International Conference of Knowledge Representation and Reasoning (KR04), 2004.

• [Franconi and Tessaris, 2004] Enrico Franconi and Sergio Tessaris. Rules and queries with ontologies: a unified logical framework. In Workshop on Principles and Practice of Semantic Web Reasoning (PPSWR’04), St. Malo, France, 2004.

• [Rosati, 1999] Riccardo Rosati. Towards expressive KR systems integrating datalog and description logics: A preliminary report. In Proc. of the 1999 International Description Logics workshop (DL99), pages 160–164, 1999.