Showing papers by "Michael J. Maher published in 1988"

Complete axiomatizations of the algebras of finite, rational and infinite trees

Abstract: Complete axiomizations for the algebras of infinite trees and infinite trees are presented. The axiomizations are parameterized by the alphabet of function symbols for both the finite trees and infinite trees. There are two main cases, depending on whether the number of function symbols is finite or infinite. In the former case an extra axiom is necessary to obtain completeness. The method of proof is an elimination of quantifiers. Although a full elimination of quantifiers is not possible, the method forms the basis of decision procedures for the theories of the corresponding algebras. As a corollary to the results in infinite trees, the elementary equivalence of the algebra of rational trees and the algebra of infinite trees is obtained. >

Equivalences of logic programs

Abstract: For applications such as deductive databases employing the Open World Assumption, failed derivations have a lesser importance. In this case, use of the identical equivalences based upon the functional semantics [P] and the logical consequences of P allows the application of two different and powerful tools to reason about programs. In particular, these equivalences seem ideal for discussing the deductive structure of such deductive databases, independent of any particular state of the database of facts.

Chapter 15 – Unification Revisited

Abstract: In the literature, unification is often treated as a simple and straightforward matter, even though it is recognized as a deep and fundamental concept. However when a thorough presentation is attempted, it is realized then that the matter is fairly subtle and treacherous. For instance, the notion of most general unifier and its property of being unique up to renaming are open to different interpretations. In fact, there are several approaches to unification based on different mathematical concepts that are not equivalent. We present the alternatives and clarify their relationships. In the process, new results are obtained related to the notions of equation solving, most specific generalization, and constraint solving. This leads to a comprehensive presentation of an elementary theory of unification.