Информационная система "Конференции"

Abstracts

Applications of logic in computer science

Two infinite structures (sets together with operations and relations) hold our attention: trees with operations of construction and real numbers with the operation of addition. The object of this paper is the study of the evaluated trees, a structure mixing the two preceding ones. After having defined the signature, the domain, the operations and the relations of this structure, we propose in the form of a set of first-order propositions, a theory T of which it is a model.

To show the completeness of our theory T, we establish a general theorem which gives a sufficient condition for the completeness of any first-order theory. This theorem uses a special quantifier, primarily asserting the existence of an infinity of individuals having a given first order property. From this theorem we show that we can extract a general algorithm for solving constraints in T.

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