Negative Reasoning Using Inheritance Lin Padgham Department of Computer and Information Science Linkoping University S-581 83 Linkoping, Sweden lin@ida.liu.se Abstract This paper presents methods of default reasoning which allow us to draw negative conclusions that are not available in some of the models for inheritance reasoning. Some of these negative conclusions are shown to be logically required, while others result from an extension of the model to include the notion of a default negative assumption. The negative default assumption operator is exactly symmetrical to positive default assumption, and supports the drawing of extra negative conclusions. It is argued that in some domains negative conclusions are extremely important. An example is given from the medical domain to illustrate the usefulness of techniques for deducing negative facts. A formal definition of the inheritance model used, which in an earlier paper by the same author [Padgham 88] was shown to resolve a number of the classical problems in the literature on inheritance reasoning, is also given. 1. Introduction Most of the literature on inheritance reasoning [Etherington 87, Fahlman 79, Touretzky 86, Sandewall 86, etc.] focusses on methods for collecting inherited information regarding an entity, in the presence of conflicting information. Conflicting information is usually of the type X is a Y, and X is not a Y. This negative information regarding what X is not is often extremely important. For example in medical diagnosis, it is often equally important to rule out certain diseases as it is to obtain a positive diagnosis. Similarly if one is reasoning about prescriptions for medical drugs, one is extremely interested in the negative information, i.e. contra-indications, or incompatibilities. It is often just this negative information which is not quite so immediate and may need to be deduced, using in part an inheritance reasoning mechanism. We present a method for doing default reasoning with an inheritance schema which allows both default and strict reasoning about negative conclusions in the same way as it does about positive conclusions. In order to present the negative reasoning we need first to present the basic model, and the reasoning methods for positive and explicit negative information. Deduction of extra negative information then follows from these. We will illustrate with some examples which are a little more complex than the usual examples found in the literature because one needs the added complexity in order to benefit from the added reasoning. We will also attempt to relate the methods to some standard examples, in order to at least explain the results within a familiar context. However the real power of these mechanisms will be seen in more complex real-world reasoning systems, for which the methods are of course intended. This work was sponsored by the Swedish Board for Technical Development. 2. Overview of The Inheritance Model The basic model is that both objects and types can be described by sets of characteristics, which can be partially ordered according to the notion of more information. Thus for an object to be a member of a particular class/type it must contain as much information as is required for the type, or more; that is it must contain at least all the characteristics required by the type. Similarly a type A is a subtype of type B if A contains all the characteristics of B, plus some extra characteristics. Formally types are points in a lattice of descriptors within which a partial order and lattice operations and are defined. In the simplest case we assume C to be the set of all characteristics, choose 1086 Commonsense Reasoning