Circumscription And Generic Mathematical Objects

Authors:
Leopoldo E. Bertossi;Raymond Reiter
Affiliations:
Pontificia Universidad Catolica de Chile, Escuela de Ingenieria, Departamento de Ciencia de la Computacion, Casilla 306, Santiago 22, Chile, e-mail: bertossi@ing.puc.cl;Department of Computer Science, University of Toronto, Toronto, Canada M5S 1A4 and The Canadian Institute for Advanced Research e-mail: reiter@ai.toronto.edu
Venue:
Fundamenta Informaticae
Year:
1994

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Abstract

We investigate the possibility of using circumscription for characterizing the concept of a generic object in the context of a formalized mathematical theory. We show that conventional circumscriptive policies do not give the intuitively expected results for elementary geometry, and that there is a common explanation for this failure and the failure of circumscription in some standard instances of commonsense reasoning. It turns out, however, that scoped circumscription does provide the right mechanism for this task.