Modeling default reasoning through A-uncertainty Pietro Baroni, Giovanni Guida Università di Brescia Dip. di Elettronica per l'Automazione Via Branze 38, 25123 Brescia, Italy e-mail: {baroni, guida}@bsing.ing.unibs.it Silvano Mussi CILEA (Consorzio Interuniversitario Lombardo per la Elaborazione Automatica) Via R. Sanzio 4, 20090 Segrate, Italy e-mail: mussi@icil64.cilea.it Abstract In this paper we present a novel approach to default reasoning, based on the concept of A- uncertainty, namely uncertainty concerning rule applicability. The paper first presents a focused analysis, based on some simple default reasoning examples, of the limitations of some well-known approaches to default reasoning. Then, the novel approach, based on the explicit representation of A-uncertainty is introduced. It is based on a concept of A-uncertainty intended as a property concerning both an inference rule and the individual to which it is applied, and it is shown to be appropriate to overcome most of the limitations found in classical approaches in a natural and effective way. A general default reasoning scheme is then proposed, which exploits the advantages of the introduced representation and sets up a promising background for efficient implementations of automated reasoning . 1. INTRODUCTION The capability of drawing defeasible conclusions in presence of partial information is a crucial factor of intelligent behavior. To achieve this capability, human beings resort to a particular kind of knowledge, called default knowledge. The most significant property of default knowledge is that it can be exploited in the reasoning process even if there is only partial information about the satisfaction of the preconditions which allow its application, on condition that there is no reason to believe that such preconditions are not satisfied. If new information becomes available from which the falsity of such preconditions can be deduced, the conclusions derived from the application of default knowledge have to be retracted. This particular form of reasoning, involving the use of default knowledge, is called default reasoning. In order to build automated reasoning systems including default reasoning capabilities, many extensions of classical logic have been proposed as models of default reasoning. Among the most notable and classic proposals in this field we mention default logic [10] and nonmonotonic logic [8]. The aim of this paper is to propose a new approach to modeling of default reasoning, relying on a different conceptual background with respect to all previous ones. The proposed approach is grounded on the concepts of A- and V-uncertainty we have introduced in a previous paper [2] and allows overcoming in a natural and effective way some conceptual and practical limitations of previous logic- based approaches. The paper is organized as follows. In section 2 we develop a conceptual analysis of default reasoning, also introducing some default reasoning cases which show significantly different features from the default examples normally found in previous literature. In section 3 we briefly review some approaches to default reasoning and we show that they are inappropriate to deal with the default reasoning cases presented in section 2. In section 4 we shortly recall the concepts of A- and V-uncertainty. In section 5 we introduce our approach to default reasoning, grounded on the concept of A-uncertainty, and we show that it allows a natural treatment of the cases presented in section 2, thus overcoming some limitations of other classical approaches. A final discussion and some conclusions are presented in section 6. 2. DEFAULT REASONING: A CONCEPTUAL ANALYSIS In a very simple and basic formulation, an inference step of default reasoning involves the two following entities: • a chunk of default knowledge, and • an individual to which such knowledge can be applied. Default knowledge concerns properties of the individual to which it can be applied and, in very general terms, it can be characterized as a form of relational knowledge, in the