A Logic for Partial System Description

Abstract

In this article, we investigate a notion of approximation based on partial descriptions of a given situation. We adopt a relative approach which focuses on the relations that exist between different partial descriptions, and propose a general algebraic framework for formalizing this notion of partial description where we take two types of relation into consideration: a partial order telling whether a partial description provides more information than another, and a notion of point of view which relates each partial description to a way of observing the system and getting information about it. We then use this framework to introduce an intuitionistic modal logic based on our notion of partial description.