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The Semantics Of Constraint Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1996
"... This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and comp ..."
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Cited by 786 (13 self)
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This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important since almost all CLP systems use an incomplete solver. Third, we give conditions on the (possibly incomplete) solver which ensure that the operational semantics is confluent, that is, has independence of literal scheduling.
Disunification: a Survey
 Computational Logic: Essays in Honor of Alan
, 1991
"... Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey the ..."
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Cited by 57 (9 self)
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Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey these works and bring them together in a same framework. R'esum'e On appelle habituellement (algorithme d') unification un algorithme de r'esolution d'une 'equation dans une alg`ebre de termes. La r'esolution de formules plus complexes, comportant en particulier des n'egations, est appel'ee ici disunification. Avec une d'efinition aussi 'etendue, de nombreux travaux peuvent etre consid'er'es comme portant sur la disunification. L'objet de cet article de synth`ese est de rassembler tous ces travaux dans un meme formalisme. Laboratoire de Recherche en Informatique, Bat. 490, Universit'e de ParisSud, 91405 ORSAY cedex, France. Email: comon@lri.lri.fr i Contents 1 Syntax 5 1.1 Basic Defini...
Solving Symbolic Ordering Constraints
, 1990
"... We show how to solve boolean combinations of inequations s ? t in the Herbrand Universe, assuming that is interpreted as a lexicographic path ordering extending a total precedence. In other words, we prove that the existential fragment of the theory of a lexicographic path ordering which extends a ..."
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Cited by 50 (11 self)
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We show how to solve boolean combinations of inequations s ? t in the Herbrand Universe, assuming that is interpreted as a lexicographic path ordering extending a total precedence. In other words, we prove that the existential fragment of the theory of a lexicographic path ordering which extends a total precedence is decidable. Keywords: simplification orderings, ordered strategies, term algebras, constraint solving. 1. Introduction The first order theory of term algebras over a language (or alphabet) with no relational symbol (other than equality) has been shown to be decidable 1;2 . See also Refs 3 and 4. Introducing into the language a binary relational symbol interpreted as the subterm ordering makes the theory undecidable 5 . Venkataraman also shows in the latter paper that the purely existential fragment of the theory, i.e. the subset of sentences whose prenex form does not contain 8, is decidable. Venkataraman was concerned with some applications in functional programm...
ModelTheoretic Methods in Combined Constraint Satisfiability
 Journal of Automated Reasoning
, 2004
"... We extend NelsonOppen combination procedure to the case of theories which are compatible with respect to a common subtheory in the shared signature. The notion of compatibility relies on model completions and related concepts from classical model theory. ..."
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Cited by 40 (10 self)
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We extend NelsonOppen combination procedure to the case of theories which are compatible with respect to a common subtheory in the shared signature. The notion of compatibility relies on model completions and related concepts from classical model theory.
Equational Formulae with Membership Constraints
 Information and Computation
, 1994
"... We propose a set of transformation rules for first order formulae whose atoms are either equations between terms or "membership constraints" t 2 i. i can be interpreted as a regular tree language (i is called a sort in the algebraic specification community) or as a tree language in any class of lang ..."
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Cited by 33 (3 self)
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We propose a set of transformation rules for first order formulae whose atoms are either equations between terms or "membership constraints" t 2 i. i can be interpreted as a regular tree language (i is called a sort in the algebraic specification community) or as a tree language in any class of languages which satisfies some adequate closure and decidability properties. This set of rules is proved to be correct, terminating and complete. This provides a quantifier elimination procedure: for every regular tree language L, the first order theory of some structure defining L is decidable. This extends the results of Mal'cev (1971), Maher (1988), Comon and Lescanne (1989). We also show how to apply our results to automatic inductive proofs in equational theories. Introduction To unify two terms s and t means to turn the equation s = t into an equivalent solved form which is either ? (this means that s = t has no solution, or, in other words, that s and t are not unifiable) or else a form...
An Improved Lower Bound for the Elementary Theories of Trees
, 1996
"... . The firstorder theories of finite and rational, constructor and feature trees possess complete axiomatizations and are decidable by quantifier elimination [15, 13, 14, 5, 10, 3, 20, 4, 2]. By using the uniform inseparability lower bounds techniques due to Compton and Henson [6], based on repr ..."
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Cited by 29 (3 self)
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. The firstorder theories of finite and rational, constructor and feature trees possess complete axiomatizations and are decidable by quantifier elimination [15, 13, 14, 5, 10, 3, 20, 4, 2]. By using the uniform inseparability lower bounds techniques due to Compton and Henson [6], based on representing large binary relations by means of short formulas manipulating with high trees, we prove that all the above theories, as well as all their subtheories, are nonelementary in the sense of Kalmar, i.e., cannot be decided within time bounded by a k story exponential function 1 exp k (n) for any fixed k. Moreover, for some constant d ? 0 these decision problems require nondeterministic time exceeding exp 1 (bdnc) infinitely often. 1 Introduction Trees are fundamental in Computer Science. Different tree structures are used as underlying domains in automated theorem proving, term rewriting, functional and logic programming, constraint solving, symbolic computation, knowledge re...
On Constructive Negation in Logic Programming
 In North American Conference on Logic Programming
, 1995
"... this paper we significantly extend Chan's approach and provide it with a more thorough theoretical foundation. ..."
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Cited by 24 (3 self)
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this paper we significantly extend Chan's approach and provide it with a more thorough theoretical foundation.
A Uniform Axiomatic View of Lists, Multisets, and Sets, and the Relevant Unification Algorithms
, 1998
"... . The rstorder theories of lists, multisets, compact lists (i.e., lists where the number of contiguous occurrences of each element is immaterial), and sets are introduced via axioms. Such axiomatizations are shown to be very wellsuited for the integration with free functor symbols governed by the ..."
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Cited by 22 (15 self)
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. The rstorder theories of lists, multisets, compact lists (i.e., lists where the number of contiguous occurrences of each element is immaterial), and sets are introduced via axioms. Such axiomatizations are shown to be very wellsuited for the integration with free functor symbols governed by the classical Clark's axioms in the context of (Constraint) Logic Programming. Adaptations of the extensionality principle to the various theories taken into account is then exploited in the design of unication algorithms for the considered data structures. All the theories presented can be combined providing frameworks to deal with We acknowledge partial support from C.N.R. Grant 97.02426.CT12, C.N.R. project SETA, and from the MURST project \Tecniche formali per la specica, l'analisi, la verica, la sintesi e la trasformazione di sistemi software". 202 Dovier, Policriti, and Rossi / A uniform axiomatic view of lists, multisets, and sets several of the proposed data structures simultan...