David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Philosophical Logic 39 (3):229 - 254 (2010)
Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is interior parthood . This choice will have the advantage that filters may be defined with respect to it, constructing “points”, as Peter Roeper has done (“Region-based topology”, Journal of Philosophical Logic , 26 (1997), 25–309). This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an approximate lattice , because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of “points” in a topological “space”.
|Keywords||Approximate lattice Filter Mereology Mereotopology Spacetime Ultrafilter|
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References found in this work BETA
Roberto Casati, Barry Smith & Achille C. Varzi (1998). Ontological Tools for Geographic Representation. In Nicola Guarino (ed.), Formal Ontology in Information Systems (FOIS). Ios Press. 77--85.
Bowman L. Clark (1985). Individuals and Points. Notre Dame Journal of Formal Logic 26 (1):61-75.
Bowman L. Clarke (1981). A Calculus of Individuals Based on ``Connection''. Notre Dame Journal of Formal Logic 22 (3):204-218.
Theodore de Laguna (1922). Point, Line, and Surface, as Sets of Solids. Journal of Philosophy 19 (17):449-461.
Peter Forrest (2007). Mereological Summation and the Question of Unique Fusion. Analysis 67 (295):237–242.
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