In the past little work has been done to characterize the models of various mereotopological systems. This thesis focuses on Asher and Vieu's first-order mereotopology which evolved from Clarke's Calculus of Individuals. Its soundness and completeness proofs with respect to a topological translation of the axioms provide only sparse insights into structural properties of the mereotopological models. To overcome this problem, we characterize these models with respect to mathematical
structures with well-defined properties - topological spaces, lattices, and graphs.
We prove that the models of the subtheory RT− are isomorphic to p-ortholattices
(pseudocomplemented, orthocomplemented). Combining the advantages of lattices
and graphs, we show how Cartesian products of finite p-ortholattices with one multiplicand being not uniquely complemented (unicomplemented) gives finite models of the full mereotopology. Our analysis enables a comparison to other mereotopologies, in particular to the RCC, of which lattice-theoretic characterizations exist.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/10432 |
| Date | 25 July 2008 |
| Creators | Hahmann, Torsten |
| Contributors | Gruninger, Michael John |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
| Format | 1445609 bytes, application/pdf |
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