Proceedings ArticleDOI
Complete axiomatizations of the algebras of finite, rational and infinite trees
Michael J. Maher
- pp 348-357
TLDR
The elementary equivalence of thegebra of rational trees and the algebra of infinite trees is obtained and forms the basis of decision procedures for the theories of the corresponding algebras.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. >read more
Citations
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Journal ArticleDOI
Constraint logic programming : A survey
Joxan Jaffar,Michael J. Maher +1 more
TL;DR: This survey of CLP is to give a systematic description of the major trends in terms of common fundamental concepts and the three main parts cover the theory, implementation issues, and programming for applications.
Book ChapterDOI
CHAPTER 6 – Rewrite Systems
TL;DR: In this paper, the authors focus on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained.
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Concurrent constraint programming
Vijay Saraswat,Martin Rinard +1 more
TL;DR: This paper presents a new and very rich class of (concurrent) programming languages, based on the notion of computing with partial information, and the concomitant notions of consistency and entailment, and develops the cc family of languages, which is very similar to Milner's CCS.
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Equational problems anddisunification
Hubert Comon,Pierre Lescanne +1 more
TL;DR: This work proposes some rules for the transformation of equational problems and studies their correctness in various models and gives completeness results with respect to some ''simple'' problems called solved forms.
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Acyclic programs
Krzysztof R. Apt,Marc Bezem +1 more
TL;DR: It is shown that the immediate consequence operator of an acyclic programP has a unique fixpointMp, which coincides with the perfect model ofP, is the unique Herbrand model of the completion ofP and can be identified with the unique fix point of the 3-valued immediate consequence operators associated withP.
References
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Book
Foundations of logic programming
TL;DR: This is the second edition of an account of the mathematical foundations of logic programming, which collects, in a unified and comprehensive manner, the basic theoretical results of the field, which have previously only been available in widely scattered research papers.
Book ChapterDOI
Negation as failure
TL;DR: It is shown that when the clause data base and the queries satisfy certain constraints, which still leaves us with a data base more general than a conventional relational data base, the query evaluation process will find every answer that is a logical consequence of the completed data base.
Proceedings ArticleDOI
Constraint logic programming
Joxan Jaffar,Jean-Louis Lassez +1 more
TL;DR: In this article, a class of logic programming languages, called CLP languages, are defined, all of which share the same essential semantic properties and are based on a unified formal semantics.
Journal ArticleDOI
An Efficient Unification Algorithm
Arabella Martelli,Ugo Montanari +1 more
TL;DR: A new unification algorithm, characterized by having the acyclicity test efficiently embedded into it, is derived from the nondeterministic one, and a PASCAL implementation is given.
Journal ArticleDOI
Initial Algebra Semantics and Continuous Algebras
TL;DR: An overview of initial algebra semantics is provided and the major technical feature is an initial continuous algebra which permits unified algebraic treatment of iterative and recursive semantic features in the same framework as more basic operations.