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Introducing OBJ
, 1993
"... This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OBJ3 is described in detail, with many examples. OBJ is a wide spectrum firstorder functional language that is rigorously based on ..."
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Cited by 135 (30 self)
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This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OBJ3 is described in detail, with many examples. OBJ is a wide spectrum firstorder functional language that is rigorously based on (order sorted) equational logic and parameterized programming, supporting a declarative style that facilitates verification and allows OBJ to be used as a theorem prover.
A New Method for Undecidability Proofs of First Order Theories
 Journal of Symbolic Computation
, 1992
"... this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction ..."
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Cited by 30 (6 self)
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this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction
Combination Techniques and Decision Problems for Disunification
 Theoretical Computer Science
"... Previous work on combination techniques considered the question of how to combine unification algorithms for disjoint equational theories E 1 ; : : : ; E n in order to obtain a unification algorithm for the union E 1 [ : : : [ E n of the theories. Here we want to show that variants of this method m ..."
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Cited by 21 (6 self)
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Previous work on combination techniques considered the question of how to combine unification algorithms for disjoint equational theories E 1 ; : : : ; E n in order to obtain a unification algorithm for the union E 1 [ : : : [ E n of the theories. Here we want to show that variants of this method may be used to decide solvability and ground solvability of disunification problems in E 1 [ : : : [E n . Our first result says that solvability of disunification problems in the free algebra of the combined theory E 1 [ : : : [E n is decidable if solvability of disunification problems with linear constant restrictions in the free algebras of the theories E i (i = 1; : : : ; n) is decidable. In order to decide ground solvability (i.e., solvability in the initial algebra) of disunification problems in E 1 [ : : : [ E n we have to consider a new kind of subproblem for the particular theories E i , namely solvability (in the free algebra) of disunification problems with linear constant restricti...
Open Problems in Rewriting
 Proceeding of the Fifth International Conference on Rewriting Techniques and Application (Montreal, Canada), LNCS 690
, 1991
"... Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27 ..."
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Cited by 19 (2 self)
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Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27, 28, 44, 56,57,76, 82, 81#; one edited collection of papers #1#; four monographs #3, 12,55,65#; and seven books #four of them still in progress# #8,9, 35, 54, 60,75, 84#. To encourage and stimulate continued progress in this area, wehave collected #with the help of colleagues# a number of problems that appear to us to be of interest and regarding whichwe do not know the answer. Questions on rewriting and other equational paradigms have been included; manyhave not aged su#ciently to be accorded the appellation #open problem". Wehave limited ourselves to theoretical questions, though there are certainly many additional interesting questions relating to applications and implementation
Feature Constraints with FirstClass Features
 Mathematical Foundations of Computer Science, Lecture Notes in Computer Science
, 1993
"... . Feature Constraint Systems have been proposed as a logical data structure for constraint (logic) programming. They provide a recordlike view to trees by identifying subtrees by keyword rather than by position. Their atomic constraints are finer grained than in the constructorbased approach. The ..."
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Cited by 10 (3 self)
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. Feature Constraint Systems have been proposed as a logical data structure for constraint (logic) programming. They provide a recordlike view to trees by identifying subtrees by keyword rather than by position. Their atomic constraints are finer grained than in the constructorbased approach. The recently proposed CFT [15] in fact generalizes the rational tree system of Prolog II. We propose a new feature constraint system EF which extends CFT by considering features as first class values. As a consequence, EF contains constraints like x[v]w where v is a variable ranging over features, while CFT restricts v to be a fixed feature symbol. We show that the satisfiability of conjunctions of atomic EFconstraints is NPcomplete. Satisfiability of quantifierfree EFconstraints is shown to be decidable, while the 9 8 9 fragment of the first order theory is undecidable. 1 Introduction Feature constraints provide records as logical data structure for constraint (logic) programmin...
Tree Automata and Automated Model Building
, 1997
"... . The use of regular tree grammars to represent and build models of formulae of firstorder logic without equality is investigated. The combination of regular tree grammars with equational constraints provides a powerful and general way of representing Herbrand models. We show that the evaluation pr ..."
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Cited by 9 (4 self)
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. The use of regular tree grammars to represent and build models of formulae of firstorder logic without equality is investigated. The combination of regular tree grammars with equational constraints provides a powerful and general way of representing Herbrand models. We show that the evaluation problem (i.e. the problem of finding the truth value of a formula in a given model) is decidable when models are represented in the way we propose. We also define a method to build such representations of models for firstorder formulae. These results are a powerful extension of our former method for simultaneous search for refutations and models. Keywords: Automated Deduction, Model Building, Tree Automata, Regular Tree Grammars. 1. Introduction The problem of building models or counterexamples of firstorder formulae is a very important one, particularly in the field of automated deduction. Besides their intrinsic interest for disproving conjectures, counterexamples (models) have numerous...
Automated Induction with Constrained Tree Automata
, 2008
"... We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, ordering ..."
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Cited by 7 (2 self)
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We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, ordering and also membership in a fixed tree language. Constrained equational axioms between constructor terms are supported and can be used in order to specify complex data structures like sets, sorted lists, trees, powerlists... Our procedure is based on tree grammars with constraints, a formalism which can describe exactly the initial model of the given specification (when it is sufficiently complete and terminating). They are used in the inductive proofs first as an induction scheme for the generation of subgoals at induction steps, second for checking validity and redundancy criteria by reduction to an emptiness problem, and third for defining and solving membership constraints. We show that the procedure is sound and refutationally complete. It generalizes former test set induction techniques and yields natural proofs for several nontrivial examples presented in the paper, these examples are difficult (if not impossible) to specify and carry on automatically with other induction procedures.
Simplifying and generalizing formulae in tableaux. Pruning the search space and building models (long version)
, 1997
"... . A powerful extension of the tableau method is described. It consists in a new simplification rule allowing to prune the search space and a new way of extracting a model from a given (possibly infinite) branch. These features are combined with a former method for simultaneous search for refutations ..."
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Cited by 5 (0 self)
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. A powerful extension of the tableau method is described. It consists in a new simplification rule allowing to prune the search space and a new way of extracting a model from a given (possibly infinite) branch. These features are combined with a former method for simultaneous search for refutations and models. The possibilities of the new method w.r.t. the original one are clearly stated. In particular it is shown that the method is able to build model for each formula having a model expressible by equational constraints. 1. Introduction The construction and the use of models or counterexamples are crucial techniques widely used in all aspects of human reasoning. In mathematics, models allow the rejection of false conjectures or help to prove theorems. Incorporating such abilities into automated theorem provers is therefore a very natural idea, which has been considered since the beginning [15, 25]. Nevertheless, it is not until the nineties that feasible methods have been proposed ...
Automated induction for complex data structures. Research Report LSV0511, Laboratoire Spécification et Vérification, 2005. personal communication
 of Joe Hendrix Adel Bouhoula and Florent Jacquemard inria00579017, version 1  22 Mar 2011
"... Abstract. We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, o ..."
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Cited by 4 (3 self)
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Abstract. We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, ordering and also membership in a fixed tree language. Constrained equational axioms between constructor terms are supported and can be used in order to specify complex data structures like sets, sorted lists, trees, powerlists... Our procedure is based on tree grammars with constraints, a formalism which can describe exactly the initial model of the given specification (when it is sufficiently complete and terminating). They are used in the inductive proofs first as an induction scheme for the generation of subgoals at induction steps, second for checking validity and redundancy criteria by reduction to an emptiness problem, and third for defining and solving membership constraints. We show that the procedure is sound and refutationally complete. It generalizes former test set induction techniques and yields natural proofs for several nontrivial examples presented in the paper, these examples are difficult to specify and carry on automatically with related induction procedures.
Negation in Combining Constraint Systems
 Communications of the ACM
, 1998
"... In a recent paper, Baader and Schulz presented a general method for the combination of constraint systems for purely positive constraints. But negation plays an important role in constraint solving. E.g., it is vital for constraint entailment. Therefore it is of interest to extend their results to t ..."
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Cited by 3 (0 self)
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In a recent paper, Baader and Schulz presented a general method for the combination of constraint systems for purely positive constraints. But negation plays an important role in constraint solving. E.g., it is vital for constraint entailment. Therefore it is of interest to extend their results to the combination of constraint problems containing negative constraints. We show that the combined solution domain introduced by Baader and Schulz is a domain in which one can solve positive and negative "mixed" constraints by presenting an algorithm that reduces solvability of positive and negative "mixed" constraints to solvability of pure constraints in the components. The existential theory in the combined solution domain is decidable if solvability of literals with socalled linear constant restrictions is decidable in the components. We also give a criterion for ground solvability of mixed constraints in the combined solution domain. The handling of negative constraints can be signific...