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Note on Prototype Revision
Renata Wassermann
Eduardo Fermé
Renata Wassermann
Eduardo Fermé
Keywords: Belief revision, Possible worlds semantics, Conceptual spaces, Sphere semantics.
Abstract: 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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Spinning Ideas, Electronic Essays
Dedicated to Peter Gärdenfors on His Fiftieth Birthday