A Note on Cumulative Stereotypical Reasoning

Abstract

Abstract. We address the problem of providing a logical characterization of reasoning based on stereotypes. Following [6] we take a semantic perspective and we base our model on a notion of semantic distance. While still leading to cumulative reasoning, our notion of distance does, unlike Lehmann's, allow reasoning under inconsistent information. Key words: Stereotypes, prototypes, cumulative reasoning, nonmonotonic logic, default-assumption logic.One important feature of intelligent reasoning consists in the capability of associating specific situations to general patterns and by doing so, extending one's initial knowledge. Reasoning based on stereotypes is a case in point. Loosely speaking, a stereotype can be thought of as an individual whose characteristics are such that it represents a typical (i.e. generic) individual of the class it belongs to. For this reason a stereotypical individual can be expected to satisfy the key properties which are typically true of the class to which the individual belongs (see Section 2 below for an example). Of course exceptions might be waiting just around the corner and an intelligent agent must be ready to face a situation in which the properties projected on a specific individual by using stereotypical information turn out not to apply. Stereotypical reasoning is therefore defeasible.The purpose of this paper is to provide a logical insight on the problem of modelling rational stereotypical reasoning. Our central idea consists in representing the latter as a two-stage inference process along the following lines. Given a piece of specific information, an agent selects among some background information available to it, those stereotypes which better fit the factual information at hand. We expect this to normally expand the initial information available to the agent. The second step is properly inferential: using the new (possibly expanded) information set the agent draws defeasible conclusions about the situation at hand. The key ingredient in the formalization of the first stage is a function which ranks the fitness of a set of stereotypes with respect to some factual information. Following [6] we interpret fitness in terms of a semantic distance function. Due to the defeasible nature of reasoning based on stereotypes, the inferential stage will have to be formalized by a non monotonic consequence relation. Since we are interested in representing rational reasoning, we shall be asking for this consequence relation to be particularly well-behaved. In our model this amount to requiring that stereotypical reasoning should be cumulative.The paper is organized as follows. Section 2 sets the stage for our discussion on stereotypes and provides a general characterization of semantic distance.