Journal of Applied Non-Classical Logics 12 (3-4):527-559 (2002)

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Abstract
This paper is a continuation of [VAK 01]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to Roeper's notion of region-based topology [ROE 97]. The similarity between the local proximity spaces of Leader [LEA 67] and local connection algebras is emphasized. Machinery, analogous to that introduced by Efremovi?c [EFR 51],[EFR 52], Smirnov [SMI 52] and Leader [LEA 67] for proximity and local proximity spaces, is developed. This permits us to give new proximity-type models of local connection algebras, to obtain a representation theorem for such algebras and to give a new shorter proof of the main theorem of Roeper's paper [ROE 97]. Finally, the notion of MVD-algebra is introduced. It is similar to Mormann's notion of enriched Boolean algebra [MOR 98], based on a single mereological relation of interior parthood. It is shown that MVD-algebras are equivalent to local connection algebras. This means that the connection relation and boundedness can be incorporated into one, mereological in nature relation. In this way a formalization of the Whiteheadian theory of space based on a single mereological relation is obtained.
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DOI 10.3166/jancl.12.527-559
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References found in this work BETA

The Calculus of Individuals and its Uses.Henry S. Leonard & Nelson Goodman - 1940 - Journal of Symbolic Logic 5 (2):45-55.
A Calculus of Individuals Based on ``Connection''.Bowman L. Clarke - 1981 - Notre Dame Journal of Formal Logic 22 (3):204-218.
Region-Based Topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
Point, Line, and Surface, as Sets of Solids.Theodore de Laguna - 1922 - Journal of Philosophy 19 (17):449-461.

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Citations of this work BETA

Mereotopology without Mereology.Peter Forrest - 2010 - Journal of Philosophical Logic 39 (3):229-254.
A Discrete Duality Between Apartness Algebras and Apartness Frames.Ivo Düntsch & Ewa Orlowska - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):213-227.
Logics for Extended Distributive Contact Lattices.T. Ivanova - 2018 - Journal of Applied Non-Classical Logics 28 (1):140-162.

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