Algebraic properties of ω-trees (I)

Abstract

In this paper we inaugurate a possible research line to study the theoretical aspects of the answer function for a master-slave system based on semantic schemas. We define the concept of ω-labeled tree as a binary, ordered and labeled tree with several features concerning the labels and order between the direct descendants of a node. The labeling operation of the nodes is guided by the mapping ω which defines the splitting operation for labels. An embedding operation of an ω-tree into another ω-tree is introduced. We prove that this operation is performed by means of an injective mapping. Based on this operation some binary relation between ω-labeled trees is defined. This is a reflexive and transitive relation, but is not antisymmetric. All the results proved in this paper and in [15] constitute the algebraic background of a forthcoming paper as we mention in the last section.