TY - GEN

T1 - A Demand-driven Algorithm for Generating Minimal Models

AU - Ben-Eliyahu-Zohary, Rachel

N1 - Publisher Copyright:
Copyright © 2000, American Association for Artificial Intelligence (www.aaai.org). All rights reserved.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The task of generating minimal models of a knowledge base is a significant computational problem in artificial intelligence. This task is at the computational heart of diagnosis systems like truth maintenance systems, and of nonmonotonic systems like autoepistemic logic, default logic, and disjunctive logic programs. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases, Ψ1, Ψ2, ..., with the following properties: first, Ψ1 is the class of all Horn knowledge bases; second, if a knowledge base T is in Ψk, then T has at most k minimal models, and all of them may be found in time O(lnk), where l is the length of the knowledge base and n the number of atoms in T; third, for an arbitrary knowledge base T, we can find the minimum k such that T belongs to Ψk in time polynomial in the size of T; and, last, where K is the class of all knowledge bases, it is the case that U∞i=1Ψi = K, that is, every knowledge base belongs to some class in the hierarchy. The algorithm is demand-driven, that is, it is capable of generating one model at a time.

AB - The task of generating minimal models of a knowledge base is a significant computational problem in artificial intelligence. This task is at the computational heart of diagnosis systems like truth maintenance systems, and of nonmonotonic systems like autoepistemic logic, default logic, and disjunctive logic programs. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases, Ψ1, Ψ2, ..., with the following properties: first, Ψ1 is the class of all Horn knowledge bases; second, if a knowledge base T is in Ψk, then T has at most k minimal models, and all of them may be found in time O(lnk), where l is the length of the knowledge base and n the number of atoms in T; third, for an arbitrary knowledge base T, we can find the minimum k such that T belongs to Ψk in time polynomial in the size of T; and, last, where K is the class of all knowledge bases, it is the case that U∞i=1Ψi = K, that is, every knowledge base belongs to some class in the hierarchy. The algorithm is demand-driven, that is, it is capable of generating one model at a time.

UR - http://www.scopus.com/inward/record.url?scp=78649885917&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:78649885917

T3 - Proceedings of the 17th National Conference on Artificial Intelligence and 12th Conference on Innovative Applications of Artificial Intelligence, AAAI 2000

SP - 267

EP - 272

BT - Proceedings of the 17th National Conference on Artificial Intelligence and 12fth Conference on Innovative Applications ofArtificial Intelligence, AAAI 2000

PB - AAAI press

T2 - 17th National Conference on Artificial Intelligence, AAA1 2000

Y2 - 30 July 2000 through 3 August 2000

ER -