Communications of the ACM
Term rewriting and all that
Expressiveness of Full First Order Constraints in the Algebra of Finite or Infinite Trees
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Proceedings of the 2006 ACM symposium on Applied computing
Theory and Practice of Logic Programming
A Full First-Order Constraint Solver for Decomposable Theories
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
A full first-order constraint solver for decomposable theories
Annals of Mathematics and Artificial Intelligence
Solving first-order constraints in the theory of the evaluated trees
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
Solving first-order constraints in the theory of the evaluated trees
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
Extension of first-order theories into trees
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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Two infinite structures (sets together with operations and relations) hold our attention here: the trees together with operations of construction and the rational numbers together with the operations of addition and substraction and a linear dense order relation without endpoints. The object of this paper is the study of the evaluated trees, a structure mixing the two preceding ones. First of all, we establish a general theorem which gives a sufficient condition for the completeness of a first-order theory. This theorem uses a special quantifier, primarily asserting the existence of an infinity of individuals having a given first order property. The proof of the theorem is nothing other than the broad outline of a general algorithm which decides if a proposition or its negation is true in certain theories. We introduce then the theory TE of the evaluated trees and show its completeness using our theorem. From our proof it is possible to extract a general algorithm for solving quantified constraints in TE .