Creating Abstractions Using Relevance Reasoning

Reasoning with multiple levels of abstraction is a powerful method of controlling problem solving in complex domains. We consider the problem of simplifying a knowledge base by creating an abstraction that is tailored for a given set of queries. Our approach is based on associating formally an abstraction with some irrelevant detail that is removed from the knowledge base. We show how creating an abstraction and determining its utility amounts to automatically deciding which aspects of a representation are irrelevant to a query. As a result, we derive a general algorithm schema for automatically generating abstractions for a query. As an instance of the schema, we describe a novel algorithm for automatically abstracting a KB by projecting out relation arguments.

[1]  Sharon Sickel,et al.  A Search Technique for Clause Interconnectivity Graphs , 1976, IEEE Transactions on Computers.

[2]  P. Pandurang Nayak,et al.  A Semantic Theory of Abstractions: A Preliminary Report , 1994 .

[3]  Craig A. Knoblock Learning Abstraction Hierarchies for Problem Solving , 1990, AAAI.

[4]  Brian Falkenhainer,et al.  Compositional Modeling: Finding the Right Model for the Job , 1991, Artif. Intell..

[5]  Alon Y. Halevy,et al.  Exploiting Irrelevance Reasoning to Guide Problem Solving , 1993, IJCAI.

[6]  Qiang Yang,et al.  The Expected Value of Hierarchical Problem-Solving , 1992, AAAI.

[7]  Catriel Beeri,et al.  Optimizing existential datalog queries , 1988, PODS.

[8]  Alon Y. Halevy,et al.  Constraints and redundancy in datalog , 1992, PODS.

[9]  Earl D. Sacerdott Planning in a hierarchy of abstraction spaces , 1973, IJCAI 1973.

[10]  Thomas Ellman,et al.  Abstraction via Approximate Symmetry , 1993, IJCAI.

[11]  R. Guha Contexts: a formalization and some applications , 1992 .

[12]  Alon Y. Halevy,et al.  Automated Model Selection for Simulation , 1994, AAAI.

[13]  Craig A. Knoblock Search Reduction in Hierarchical Problem Solving , 1991, AAAI.

[14]  David A. Plaisted,et al.  Theorem Proving with Abstraction , 1981, Artif. Intell..

[15]  Bart Selman,et al.  Knowledge Compilation using Horn Approximations , 1991, AAAI.

[16]  Alon Y. Levy Irrelevance Reasoning in Knowledge Based Systems , 2013 .

[17]  Josh Tenenberg Abstracting First-Order Theories , 1990 .

[18]  Robert A. Kowalski,et al.  A Proof Procedure Using Connection Graphs , 1975, JACM.