Results 11 
19 of
19
A Tableau Calculus for Combining NonDisjoint Theories
 In Uwe Egly and Christian G. Fermuller, editors, Automated Reasoning with Analytic
, 2002
"... The NelsonOppen combination method combines ground satis ability checkers for rstorder theories satisfying certain conditions into a single ground satis ability checker for the union theory. The most signi cant restriction that the combined theories must satisfy, for the NelsonOppen combi ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
The NelsonOppen combination method combines ground satis ability checkers for rstorder theories satisfying certain conditions into a single ground satis ability checker for the union theory. The most signi cant restriction that the combined theories must satisfy, for the NelsonOppen combination method to be applicable, is that they must have disjoint signatures. Unfortunately, this is a very serious restriction since many combination problems concern theories over nondisjoint signatures.
Combining Constraint Solving
, 2001
"... this paper. On the one hand, dening a semantics for the combined system may depend on methods and results from formal logic and universal algebra. On the other hand, an ecient combination of the actual constraint solvers often requires the possibility of communication and cooperation between the sol ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
this paper. On the one hand, dening a semantics for the combined system may depend on methods and results from formal logic and universal algebra. On the other hand, an ecient combination of the actual constraint solvers often requires the possibility of communication and cooperation between the solvers.
HigherOrder Equational Unification via Explicit Substitutions
 in Proceedings of the tenth UNIF Workshop
, 1996
"... . We show how to reduce the unification problem modulo fij conversion and a firstorder equational theory E, into a firstorder unification problem in a union of two nondisjoint equational theories including E and a calculus of explicit substitutions. A rulebased unification procedure in thi ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
. We show how to reduce the unification problem modulo fij conversion and a firstorder equational theory E, into a firstorder unification problem in a union of two nondisjoint equational theories including E and a calculus of explicit substitutions. A rulebased unification procedure in this combined theory is described and may be viewed as an extension of the one initially designed by G. Dowek, T. Hardin and C. Kirchner for performing unification of simply typed terms in a firstorder setting via the oecalculus of explicit substitutions. Additional rules are used to deal with the interaction between E and oe. 1 Introduction Unification modulo an equational theory plays an important role in automated deduction and in logic programming systems. For example, Prolog[NM88] is based on higherorder unification, ie. unification modulo the fijconversion. In order to design more expressive higherorder logic programming systems enhanced with a firstorder equational theory E,...
Combining Decision Procedures for Positive Theories Sharing Constructors
 Rewriting Techniques and Applications, Lecture Notes in Computer Science
, 2002
"... This paper addresses the following combination problem: given two equational theories E and E2 whose positive theories are decidable, how can one obtoJn a decision procedure for the positive theory of E U E27 For theories over disjoint signatures, this problem was solved by Baader and Schulz in ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This paper addresses the following combination problem: given two equational theories E and E2 whose positive theories are decidable, how can one obtoJn a decision procedure for the positive theory of E U E27 For theories over disjoint signatures, this problem was solved by Baader and Schulz in 1995. This paper is a first step towards extending this result to the case of theories sharing constructors. Since there is a close connection between positive theories and unification problems, this also extends to the nondisjoint case the work on combining decision procedures for unification modulo equational theories.
Combining NonDisjoint Theories
 University of Siena, Italy
, 2001
"... In this paper we present a new method for combining ground decision procedures for rstorder theories over nondisjoint signatures. ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
In this paper we present a new method for combining ground decision procedures for rstorder theories over nondisjoint signatures.
Path Rewriting and Combined Word Problems
, 2000
"... . We give an algorithm solving combined word problems (over non necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying KnuthBendix completion procedure to presenta ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
. We give an algorithm solving combined word problems (over non necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying KnuthBendix completion procedure to presentations of pushouts among categories with products. It applies to pairs of theories which are both constructible over their common reduct (on which we do not make any special assumption) . Lavoro svolto nell'ambito del progetto MURST \Logica". 1 1 Introduction An essential problem in automated deduction consists in integrating theorem provers which are able to perform separated tasks. In the eld of equational logic, this leads in particular to the following question: suppose you are able to solve word problems for theories T 1 ; T 2 ; can you solve word problem for T 1 [ T 2 ? Better, can you design an algorithm taking as input two arbitrary algorithms for word problems for T 1 and T 2...
Combining Theories Sharing Dense Orders
, 2003
"... The NelsonOppen combination method combines decision procedures for firstorder theories satisfying certain conditions into a single decision procedure for the union theory. The NelsonOppen combination method can be applied only if the signatures of the combined theories are disjoint. Combination ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The NelsonOppen combination method combines decision procedures for firstorder theories satisfying certain conditions into a single decision procedure for the union theory. The NelsonOppen combination method can be applied only if the signatures of the combined theories are disjoint. Combination tableaux (Ctableaux) are an extension of Smullyan tableaux for combining firstorder theories whose signatures may not be disjoint. Ctableaux are sound and complete, but not terminating in general. In this paper we show that, when we combine firstorder theories that share the theory of dense order, Ctableaux can be made terminating without sacrificing completeness. Thus, Ctableaux provide a decision procedure for the combination of firstorder theories sharing the theory of dense order.
On Decidability of Unifiability modulo Rewrite Systems
, 1996
"... . The goal of this paper is to study the decidability of unifiability in theories represented by confluent constructorbased rewrite systems. We propose four additional restrictions on the rewrite system and the goal to be unified, and show that if only three of them are satisfied then unifiability ..."
Abstract
 Add to MetaCart
. The goal of this paper is to study the decidability of unifiability in theories represented by confluent constructorbased rewrite systems. We propose four additional restrictions on the rewrite system and the goal to be unified, and show that if only three of them are satisfied then unifiability is undecidable. Then we give a decision algorithm applicable when the four restrictions are satisfied. This algorithm generates a new kind of tree grammar as finite representation for the (possibly infinite) set of solutions. 1 Introduction Constraint Programming has known an intensive development in the last decade, in particular with Constraint Logic Programming [8] because it is a powerful paradigm to prune significantly the search space when solving a problem and to represent the solutions. In this kind of programming it is essential to decide whether the constraint is satisfiable or not and to give a representation of its set of solutions. Some work have been done to find efficient al...
Hierarchical Combination of Unification
"... A critical question in unification theory is how to obtain a unification algorithm for the combination of nondisjoint equational theories when there exists unification algorithms for the constituent theories. The problem is known to be difficult and can easily be seen to be undecidable in the gener ..."
Abstract
 Add to MetaCart
A critical question in unification theory is how to obtain a unification algorithm for the combination of nondisjoint equational theories when there exists unification algorithms for the constituent theories. The problem is known to be difficult and can easily be seen to be undecidable in the general case. Therefore, previous work has focused on identifying specific conditions