A Note on Prototype Revision

Renata Wassermann
Eduardo Fermé

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Keywords: Belief revision, Possible worlds semantics, Conceptual spaces, Sphere semantics.

: The idea of this paper is to apply methods developed in the context of belief revision in order to accommodate new information about concepts. Grove has given a model for belief revision based on a family of concentric spheres around a given belief set K. Each sphere represents a possible weakening of K, that is, the set of possible worlds obtained by giving up some information in K. Since we are interested in revision of concepts, we would like to change perspective. We are dealing with (partial) representations of objects. We find it associate with the description a set of objects satisfying it. These are all the objects the agent takes for possible given the description. Following Gärdenfors, we consider objects to be a point in a multidimensional space. A concept is a convex region of a multidimensional space. Each concept comes equipped with a family of spheres, that represent possible "weakenings" of the concept, that is, sets of objects that satisfy only part of the description. Moreover each concept contains an internal sphere representing its prototypical objects. We will examine two approaches for the revision of prototypes. First we will consider that, besides the spheres around K, the description of the concept, we have one internal sphere which represents the prototypical region, described by P. We give AGM-style characterizations for the revision of concepts and prototypes in terms of spheres, rationality postulates and partial meet revision. Next, we examine what happens when we allow for more spheres between P and K.

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Renata Wassermann

Eduardo Fermé

Spinning Ideas, Electronic Essays
Dedicated to Peter Gärdenfors on His Fiftieth Birthday