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FULL MEREOGEOMETRIES

Published online by Cambridge University Press:  18 May 2010

STEFANO BORGO  and
CLAUDIO MASOLO
STEFANO BORGO*
Affiliation:
National Research Council, Institute of Cognitive Sciences and Technologies – ISTC–CNR, Laboratory for Applied Ontology and KRDB, Free University of Bolzano
CLAUDIO MASOLO*
Affiliation:
National Research Council, Institute of Cognitive Sciences and Technologies – ISTC–CNR, Laboratory for Applied Ontology
*
*NATIONAL RESEARCH COUNCIL, INSTITUTE OF COGNITIVE SCIENCES AND TECHNOLOGIES – ISTC–CNR, LABORATORY FOR APPLIED ONTOLOGY, POVO (TRENTO), ITALY E-mail:borgo@loa-cnr.it KRDB, FREE UNIVERSITY OF BOLZANO, BOZEN-BOLZANO, ITALY
*NATIONAL RESEARCH COUNCIL, INSTITUTE OF COGNITIVE SCIENCES AND TECHNOLOGIES – ISTC–CNR, LABORATORY FOR APPLIED ONTOLOGY, POVO (TRENTO), ITALY E-mail:borgo@loa-cnr.it KRDB, FREE UNIVERSITY OF BOLZANO, BOZEN-BOLZANO, ITALY
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Abstract

We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to isolate comparable models for each theory. Relying on the chosen interpretations, we introduce the notion of environment structure, that is, a minimal structure that contains a (sub)structure for each theory. In particular, in the case of mereogeometries, the domain of an environment structure is composed of particular subsets of Rn. The comparison of mereogeometrical theories within these environment structures shows dependencies among primitives and provides (relative) definitional equivalences. With one exception, we show that all the theories considered are equivalent in these environment structures.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 4 , December 2010 , pp. 521 - 567
Copyright
Copyright © Association for Symbolic Logic 2010

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