Artificial Intelligence
Artificial Intelligence
Artificial Intelligence
Flow Analysis of Computer Programs
Flow Analysis of Computer Programs
Compiler Construction
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Truth Maintenance Systems for Problem Solving
Truth Maintenance Systems for Problem Solving
Principles of Compiler Design (Addison-Wesley series in computer science and information processing)
Principles of Compiler Design (Addison-Wesley series in computer science and information processing)
A mathematical theory of global program optimization (Prentice-Hall series in automatic computation)
A mathematical theory of global program optimization (Prentice-Hall series in automatic computation)
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
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We have recast the problem of truth maintenance in a setting of algebraic equations over Boolean lattices. If a method of labeling propositions to justify them according to some reasoning agent's constraints of belief happens to conform to the postulates of Boolean lattices, the labeling system can be reformulated as an algebraic equation solving system. All truth maintenance systems known to us can be so reformulated. This note summarizes our investigations into the existence and structure of solutions of these algebraic systems. Our central result is a unique factorization theorem for lattice equational systems and their solutions. Our theoretical results are interpreted to compare various styles of truth maintenance and to reveal certain computational difficulties implicit in the algebraic structure of truth maintenance.