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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/10432

Title: Model-Theoretic Analysis of Asher and Vieu's Mereotopology
Authors: Hahmann, Torsten
Advisor: Gruninger, Michael John
Department: Computer Science
Keywords: mereotopology
representation theorem
pseudocomplemented lattice
orthocomplemented lattice
first-order ontology
characterization as graphs of lattices
connection structure
characterization up to isomorphism
axiomatic theory
Issue Date: 25-Jul-2008
Abstract: 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.
URI: http://hdl.handle.net/1807/10432
Appears in Collections:Master
Department of Computer Science - Master theses

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