Algebraic Structure of Some Learning Systems

: Our goal is to define some general properties of the representation languages --- i.e. lattice structures, distributive lattice structures, cylindric algebras...---, on which generalization algorithms could be related. This paper introduces a formal framework providing a clear description of the version space. It is of great theoretical interest since it makes the generalization and the comparison of many machines learning algorithms possible. Moreover, it could lead to reconsider some aspects of the classical description of the version space. In this paper, we shall restrict the scope of investigation to lattices, i.e., to cases where there exists one and only one generalization for any set of examples. More precisely we take into account a particular kind of lattices: Brouwerian lattices. It is shown that a particularly interesting case covered by this restriction is the product of hierarchical posets which is equivalent to the conjonction of tree structured or linearly ordered att..