The cube lattice model and its applications

The aim of this article is to describe a basic algebraic structure on conjunctions of literals. As far as knowledge representation is concerned, the comparison of different pieces of information is a pivotal question; generally, the classical set operators (inclusion, union, intersection, subtraction) are used at least as a metaphorical model. In many applications, the core problem is the representation of actual data or information for which the basic unit of knowledge to represent is a conjunction of properties (while traditionally, AI is devoted to solving models for which the basic unit is a disjunction of properties, i.e., clauses). A specific model, called the cube model has been designed so as to capture the extension of the natural set operators to a lattice on conjunctions of first order literals. This paper is organized as follows: after a description of the origin and the postulates of the model, i.e., a need for a formal structure for knowledge fusion, the Cube model is described. Then applications are detailed: the Cubical Formal Concept Analysis, the Cubical Rule Induction, and the Reasoning tracking.