Ideal Refinement of Descriptions in AL-Log

This paper deals with learning in \(\mathcal{AL}\)-log, a hybrid language that merges the function-free Horn clause language Datalog and the description logic \(\mathcal{ALC}\). Our application context is descriptive data mining. We introduce \(\mathcal{O}\)-queries, a rule-based form of unary conjunctive queries in \(\mathcal{AL}\)-log, and a generality order ≽ B for structuring spaces of \(\mathcal{O}\)-queries. We define a (downward) refinement operator ρ O for ≽ B -ordered spaces of \(\mathcal{O}\)-queries, prove its ideality and discuss an efficient implementation of it in the context of interest.

[1]  Alan M. Frisch.  The Substitutional Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning , 1991, Artif. Intell..

[2]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

[3]  Francesca A. Lisi,et al.  Object Identity as Search Bias for Pattern Spaces , 2002, ECAI.

[4]  Donato Malerba,et al.  Bridging the Gap between Horn Clausal Logic and Description Logics in Inductive Learning , 2003, AI*IA.

[5]  Francesco M. Donini,et al.  AL-log: Integrating Datalog and Description Logics , 1998, Journal of Intelligent Information Systems.

[6]  Jörg-Uwe Kietz,et al.  Learnability of Description Logic Programs , 2002, ILP.

[7]  C. Eline Rouveirol,et al.  Towards Learning in Carin-aln , 2000 .

[8]  Alex Borgiday.  On the Relative Expressiveness of Description Logics and Predicate Logics , 1996 .

[9]  Shan-Hwei Nienhuys-Cheng,et al.  Foundations of Inductive Logic Programming , 1997, Lecture Notes in Computer Science.

[10]  Franco Turini,et al.  AI*IA 2003: Advances in Artificial Intelligence , 2003, Lecture Notes in Computer Science.

[11]  Donato Malerba,et al.  Towards Object-Relational Data Mining , 2003, SEBD.

[12]  Heikki Mannila,et al.  Levelwise Search and Borders of Theories in Knowledge Discovery , 1997, Data Mining and Knowledge Discovery.

[13]  Hannu Toivonen,et al.  Discovery of frequent DATALOG patterns , 1999, Data Mining and Knowledge Discovery.

[14]  Alan M. Frisch.  Sorted Downward Refinement: Building Background Knowledge into a Refinement Operator for Inductive Programming , 1999, ILP.

[15]  Richard B. Scherl,et al.  A Bibliography on Hybrid Reasoning , 1991, AI Mag..

[16]  Liviu Badea,et al.  Refinement Operators Can Be (Weakly) Perfect , 1999, ILP.

[17]  Anthony G. Cohn,et al.  Thoughts and Afterthoughts on the 1988 Workshop on Principles of Hybrid Reasoning , 1991, AI Mag..

[18]  Wray L. Buntine.  Generalized Subsumption and Its Applications to Induction and Redundancy , 1986, Artif. Intell..

[19]  Katharina Morik,et al.  A Polynomial Approach to the Constructive Induction of Structural Knowledge , 2004, Machine Learning.

[20]  Frank van Harmelen,et al.  Proceedings of the 15th European Conference on Artificial Intelligence , 2002 .

[21]  Donato Malerba,et al.  A Logic Framework for the Incremental Inductive Synthesis of Datalog Theories , 1997, LOPSTR.

[22]  Raymond Reiter,et al.  Equality and Domain Closure in First-Order Databases , 1980, JACM.

[23]  William W. Cohen,et al.  Learning the Classic Description Logic: Theoretical and Experimental Results , 1994, KR.

[24]  Matthias Jarke,et al.  Logic Programming and Databases , 1984, Expert Database Workshop.

[25]  Alan Bundy,et al.  Logic Program Synthesis via Proof Planning , 1992, LOPSTR.

[26]  Liviu Badea,et al.  A Refinement Operator for Description Logics , 2000, ILP.

[27]  Alon Y. Halevy,et al.  Combining Horn Rules and Description Logics in CARIN , 1998, Artif. Intell..