A note on the axiomatics of theories in parthood

Authors:
Carsten Pontow
Affiliations:
Institute for Medical Knowledge Representation and Visualization, University for Health Informatics and Technology Tyrol (UMIT), Innrain 98, A-6020 Innsbruck, Austria
Venue:
Data & Knowledge Engineering
Year:
2004

Citing 3
Cited 2

Parts, wholes, and part-whole relations: the prospects of mereotopology

Data & Knowledge Engineering - Special issue on modeling parts and wholes
Mereotopology: a theory of parts and boundaries

Data & Knowledge Engineering - Special issue on modeling parts and wholes
Part-whole relations in object-centered systems: an overview

Data & Knowledge Engineering - Special issue on modeling parts and wholes

A mathematical analysis of theories of parthood

Data & Knowledge Engineering
A framework in prolog for computing structural relationships

Data & Knowledge Engineering

Quantified Score

Hi-index	0.00

Visualization

Abstract

We discuss the axiomatic base of some of the most prominent theories of parthood (mereologies), in particular of General (Classical) Extensional Mereology (GEM). Parthood is axiomatized in GEM as a partial ordering to which a supplementation axiom and a general summing axiom are added. In this paper, we disprove the common assumption that it makes no difference for the strength of the resulting theory whether in the above framework the so-called Strong or the Weak Supplementation Principle is taken as supplementation axiom. We further show some more counterexamples to common assertions from literature concerning the interdependance of some of the axioms of the various mereological theories. It turns out that only the Strong Supplementation Principle is sufficient to fit the theories with a strong kind of extensionality.