Mereotopology without Mereology.
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)...
| Published in: | Journal of Philosophical Logic Vol. 39; no. 3; pp. 229 - 255 |
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| Format: | Article |
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Springer Nature
Jun2010
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=50328236&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 50328236 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Jun2010 vid: 39 iid: 3 pid: 237 pub: Springer Nature artinfo: ui: 50328236 10.1007/s10992-010-9130-x ppf: 229 ppct: 26 formats: fmt: @attributes: type: P size: 329KB tig: atl: Mereotopology without Mereology. aug: au: Forrest, Peter affil: Discipline of Philosophy, School of Humanities, University of New England, Armidale, NSW 2351, Australia. su: Whole & parts (Philosophy) Categories (Philosophy) Quantity (Philosophy) Axiom of choice Logic sug: subj: Whole & parts (Philosophy) Categories (Philosophy) Quantity (Philosophy) Axiom of choice Logic keyword: Approximate lattice Filter Mereology Mereotopology Spacetime Ultrafilter ab: 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”. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2010. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2010 holdings: @attributes: islocal: N |
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