-1- A robust logic for rule-based reasoning under uncertainty Simon Parsons Department of Electronic Engineering, Queen Mary and Westfield College, Mile End Road, London, E1 4NS, United Kingdom. Miroslav Kubat Computer Centre, Technical University of Brno, Udolni 19, 60200 Brno, Czechoslovakia. Mirko Dohnal Advanced Computation Laboratory, Imperial Cancer Research Fund, Lincoln’s Inn Fields, London WC2A 3PX, United Kingdom. Abstract Reasoning with uncertain information is a problem of key importance when dealing with real life knowledge. The more information required by the procedure used to handle the knowledge, the higher the probability of failure of the reasoning system. The theory of rough sets [Pawlak 1982] is not information intensive and is thus a good basis for reasoning in domains where knowledge is sparse. We present an introduction to a logic based on rough set theory that is suitable for reasoning under uncertainty. We introduce inference rules analogous to those of classical logic, and demonstrate their effectiveness in rule based reasoning. 1. Introduction Any system designed to reason about the real world must, perforce, be capable of dealing with uncertain information, that is information whose certainty may not be completely established, and incomplete knowledge about its domain. This is a direct consequence of the complexity of the real world and the finite size of the knowledge base that such a system has at its disposal. A number of mathematical formalisms have been developed to cope with uncertainty in knowledge base systems [Saffiotti 1987], and most have been demonstrated on a number of reasoning tasks. These formalisms suffer from a number of disadvantages. The severest of these is that they are all very information intensive; they all require large amounts of precise information in order to deal with uncertainty. This means that the truth value of the relations between variables are required in the form of grades of membership and probability distributions. These values are often unknown, or expensive to obtain, and methods that are not information intensive are often desirable. Rough set theory seems to solve the problem of information intensity, enabling us to avoid the paradox of performing precise calculations with imprecise data. 2. Rough set theory Rough sets, originally introduced by Pawlak [1982], have been further developed and applied to a number of problems by various authors, [Orlowska and Pawlak 1984], [Farias del Cerro and Orlowska 1985], and [Wong et al 1986]. Here we discuss the basic ideas behind the theory.