A Logic of Propositional Variations and Its Application to Case-Based Reasoning

Propositional logic (as other logics) can be seen as a way to represent sets of states of the world (by the sets of models of formulas). Representation of variations from a set of states of the world to another is motivated by studies on case-based reasoning (CBR): the comparison of two problems and the way a solution is transformed into another solution can be seen as variations from a set of states to another. This has led to a notation for representing these variations (a syntax) and this article studies how to associate to this notation a semantics based on model theory in which an interpretation is an ordered pair of interpretations in propositional logic. The article presents a classical study of this logic (syntax, semantics, properties, a formal system, etc.). It also explains how CBR can benefit from this logic, in particular through the representation of adaptation rules and to a case-based inference algorithm using such rules.