A mathematical analysis of theories of parthood

Authors:
Carsten Pontow;Rainer Schubert
Affiliations:
Institute for Biomedical Image Analysis, University for Health Sciences, Medical Informatics and Technology (UMIT), Eduard Wallnöfer-Zentrum I, Hall in Tyrol, Austria;Institute for Biomedical Image Analysis, University for Health Sciences, Medical Informatics and Technology (UMIT), Eduard Wallnöfer-Zentrum I, Hall in Tyrol, Austria
Venue:
Data & Knowledge Engineering
Year:
2006

Citing 7
Cited 1

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
Formalization of the Whole-Part Relationship in the Unified Modeling Language

IEEE Transactions on Software Engineering
What is This Thing Called Aggregation?

TOOLS '99 Proceedings of the Technology of Object-Oriented Languages and Systems
A note on the axiomatics of theories in parthood

Data & Knowledge Engineering
Black and white diamonds

UML'99 Proceedings of the 2nd international conference on The unified modeling language: beyond the standard

A framework in prolog for computing structural relationships

Data & Knowledge Engineering

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a mathematical analysis of different formal ontological theories of parthood (mereologies). We summarize variants of the theory of General Extensional Mereology (GEM) and compare them with their abstract mathematical counterpart, set theory. In particular, we prove by set theoretical means that there exists a model of GEM where arbitrary summation of entities is not possible. Further, we use Stone's duality theory for Boolean algebras to classify models of the different mereologies.