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31
Tiebout/TaxCompetition Model
 Journal of Public Economics, August
"... delivery of the gax gene inhibits vessel stenosis in a rabbit ..."
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delivery of the gax gene inhibits vessel stenosis in a rabbit
Dominance Constraints in Context Unification
, 1998
"... Tree descriptions based on dominance constraints are popular in several areas of computational linguistics including syntax, semantics, and discourse. Tree descriptions in the language of context unification have attracted some interest in unification and rewriting theory. Recently, dominance constr ..."
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Tree descriptions based on dominance constraints are popular in several areas of computational linguistics including syntax, semantics, and discourse. Tree descriptions in the language of context unification have attracted some interest in unification and rewriting theory. Recently, dominance constraints and context unification have both been used in different underspecified approaches to the semantics of scope, parallelism, and their interaction. This raises the question whether both description languages are related. In this paper, we show for a first time that dominance constraints can be expressed in context unification. We also prove that dominance constraints extended with parallelism constraints are equal in expressive power to context unification.
Linear SecondOrder Unification and Context Unification with TreeRegular Constraints
 Proc. of the 11th Int. Conference on Rewriting Techniques and Applications (RTA’2000), volume 1833 of LNCS
, 2000
"... Linear SecondOrder Unification and Context Unification are closely related problems. However, their equivalence was never formally proved. Context unification is a restriction of linear secondorder unification. Here we prove that linear secondorder unification can be reduced to context unificatio ..."
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Linear SecondOrder Unification and Context Unification are closely related problems. However, their equivalence was never formally proved. Context unification is a restriction of linear secondorder unification. Here we prove that linear secondorder unification can be reduced to context unification with treeregular constraints. Decidability of context unification is still an open question. We comment on the possibility that linear secondorder unification is decidable, if context unification is, and how to get rid of the treeregular constraints. This is done by reducing rankbound treeregular constraints to wordregular constraints.
Calculating ChurchRosser Proofs in Kleene Algebra
 Relational Methods in Computer Science, 6th International Conference, volume 2561 of LNCS
, 2002
"... We prove ChurchRosser theorems for nonsymmetric transitive relations, quasiorderings and equations in Kleene algebra. Proofs are simple, rigorous and general, using solely algebraic properties of the regular operations. They are fixed pointbased, inductionfree and often amenable to automata. The ..."
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We prove ChurchRosser theorems for nonsymmetric transitive relations, quasiorderings and equations in Kleene algebra. Proofs are simple, rigorous and general, using solely algebraic properties of the regular operations. They are fixed pointbased, inductionfree and often amenable to automata. They are mere calculations as opposed to deduction and in particular suited to automation. In the ChurchRosser proofs for the calculus, the term and algebra part are cleanly separated. In all our considerations, Kleene algebra is an excellent means of abstraction.
Context unification and traversal equations
 In: Proc. of the 12th International Conference on Rewriting Techniques and Applications (RTA’01
, 2001
"... Abstract. Context unification was originally defined by H. Comon in ICALP’92, as the problem of finding a unifier for a set of equations containing firstorder variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are secon ..."
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Abstract. Context unification was originally defined by H. Comon in ICALP’92, as the problem of finding a unifier for a set of equations containing firstorder variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are secondorder variables that are restricted to be instantiated by linear terms (a linear term is a λexpression λx1 ···λxn.t where every xi occurs exactly once in t). In this paper, we prove that, if the so called rankbound conjecture is true, then the context unification problem is decidable. This is done reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permutations) and then, reducing traversal equations to word equations with regular constraints. 1
On Unification Problems in Restricted SecondOrder Languages
 In Annual Conf. of the European Ass. of Computer Science Logic (CSL98
, 1998
"... We review known results and improve known boundaries between the decidable and the undecidable cases of secondorder unification with various restrictions on secondorder variables. As a key tool we prove an undecidability result that provides a partial solution to an open problem about simultaneous ..."
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We review known results and improve known boundaries between the decidable and the undecidable cases of secondorder unification with various restrictions on secondorder variables. As a key tool we prove an undecidability result that provides a partial solution to an open problem about simultaneous rigid Eunification.
Towards Specifying with Inclusions
, 1997
"... In this article we present a functional specification language based on inclusions between set expressions. Instead of computing with data individuals we deal with their classification into sets. The specification of functions and relations by means of inclusions can be considered as a generalizatio ..."
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In this article we present a functional specification language based on inclusions between set expressions. Instead of computing with data individuals we deal with their classification into sets. The specification of functions and relations by means of inclusions can be considered as a generalization of the conventional algebraic specification by means of equations. The main aim of this generalization is to facilitate the incremental refinement of specifications. Furthermore, inclusional specifications admit a natural visual syntax which can also be used to visualize the reasoning process. We show that reasoning with inclusions is well captured by birewriting, a rewriting technique introduced by Levy and Agust'i [15]. However, there are still key problems to be solved in order to have executable inclusional specifications, necessary for rapid prototyping purposes. The article mainly points to the potentialities and difficulties of specifying with inclusions.
Deriving Focused Calculi For Transitive Relations
 Rewriting Techniques and Applications, 12th International Conference, volume 2051 of LNCS
, 2001
"... We propose a new method for deriving focused ordered resolution calculi, exemplified by chaining calculi for transitive relations. Previously, inference rules were postulated and a posteriori verified in semantic completeness proofs. We derive them from the theory axioms. Completeness of our calculi ..."
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We propose a new method for deriving focused ordered resolution calculi, exemplified by chaining calculi for transitive relations. Previously, inference rules were postulated and a posteriori verified in semantic completeness proofs. We derive them from the theory axioms. Completeness of our calculi then follows from correctness of this synthesis. Our method clearly separates deductive and procedural aspects: relating ordered chaining to KnuthBendix completion for transitive relations provides the semantic background that drives the synthesis towards its goal. This yields a more restrictive and transparent chaining calculus. The method also supports the development of approximate focused calculi and a modular approach to theory hierarchies.
Structures for abstract rewriting
, 2007
"... When rewriting is used to generate convergent and complete rewrite systems in order to answer the validity problem for some theories, all the rewriting theories rely on a same set of notions, properties and methods. Rewriting techniques have mainly been used to answer the validity problem of equat ..."
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When rewriting is used to generate convergent and complete rewrite systems in order to answer the validity problem for some theories, all the rewriting theories rely on a same set of notions, properties and methods. Rewriting techniques have mainly been used to answer the validity problem of equational theories, that is to compute congruences. However, recently, they have been extended in order to be applied to other algebraic structures such as preorders and orders. In this paper, we investigate an abstract form of rewriting, by following the paradigm of “logicalsystem independency”. To achieve this purpose, we provide a few simple conditions (or axioms) under which rewriting (and then the set of classical properties and methods) can be modeled, understood, studied, proven and generalized. This enables us to extend rewriting techniques to other algebraic structures than congruences and preorders such as congruences closed under monotonicity and modusponens. Finally, we introduce convergent rewrite systems that enable one to describe deduction procedures for their corresponding theory, and propose a KnuthBendix style completion procedure in this abstract framework.
Theorem Proving with Transitive Relations from a Practical Point of View
 Research Report IIIA 95/12, Institut d'Investigaci'o en Intel\Deltalig`encia Artificial (CSIC
, 1995
"... Rewrite techniques have been typically applied to reason with the equality relation and have turned out to be among the more successful approaches to equational theorem proving. In fact, it is not only in reasoning with the equality relation where these techniques naturally apply, but in reasoning w ..."
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Cited by 3 (3 self)
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Rewrite techniques have been typically applied to reason with the equality relation and have turned out to be among the more successful approaches to equational theorem proving. In fact, it is not only in reasoning with the equality relation where these techniques naturally apply, but in reasoning with arbitrary, probably nonsymmetric, transitive relations, being the equality relation just a special case of monotone transitive relation, which is also symmetric. The work done so far in applying rewrite techniques to arbitrary transitive relations showed several important differences with the equational case. Although most equational results can be extended to nonsymmetric relations, new problems appear which must be solved in a quite different way. In this paper we review the use of rewrite techniques for reasoning with arbitrary possibly nonsymmetric transitive relations and we analyze the reasons why an efficient treatment of this generalization to nonsymmetric transitive relations...