# Individuals and points

@article{Clarke1985IndividualsAP, title={Individuals and points}, author={Bowman L. Clarke}, journal={Notre Dame J. Formal Log.}, year={1985}, volume={26}, pages={61-75} }

The concept of a point has been of perpetual interest to philosophers and mathematicians alike. Contemporary mathematicians and philosophers have approached the subject in three ways: One is to take as basic individuals, volumes [10], regions [18], lumps [8], or spheres [14], and to define points in terms of sets of nested individuals by way of a relation, contained in the interior of [10], nontangential part of [18], completely contained in [8], or concentric with [14]. Another technique is to…

## 173 Citations

### Expressivity in polygonal, plane mereotopology

- PhilosophyJournal of Symbolic Logic
- 2000

It is shown that infinitary versions of these languages are adequate to express (in a sense made precise below) all topological relations over the domain of polygons in the closed plane.

### Mereotopology without Mereology

- PhilosophyJ. Philos. Log.
- 2010

This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice.

### Modes of Connection

- Mathematics
- 1999

A connection based approach to common-sense topological description and reasoning. The support of the EPSRC under grants GR/K65041 and GR/M56807 is gratefully acknowledged. We are also grateful for…

### Chapter 1 DISCRETE SPATIAL MODELS

- Mathematics
- 2006

1. Introduction By " discreteness " of a spatial model we generally understand that in any bounded neighbourhood, or (bounded) region, there are only finitely many elements of the carrier of the…

### Parthood and Convexity as the Basic Notions of a Theory of Space

- PhilosophyLQMR@FedCSIS
- 2015

A deductive system of geometry is presented which is based on atomistic mereology ("mereology with points") and the notion of convexity. The system is formulated in a liberal many- sorted logic which…

### A Proximity Approach to Some Region-Based Theories of Space

- MathematicsJ. Appl. Non Class. Logics
- 2002

It is shown that MVD-algebra are equivalent to local connection algebras, which means that the connection relation and boundedness can be incorporated into one, mereological in nature relation and a formalization of the Whiteheadian theory of space based on a single mereological relation is obtained.

### A Complete Axiom System for Polygonal Mereotopology of the Real Plane

- MathematicsJ. Philos. Log.
- 1998

A calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities in which polygonal open subsets of the real plane serve as elements of the domain is presented.

### A Lattice Theoretic Account of Spatial Regions Draft Version { 25th July 1997

- Mathematics
- 1997

There have been several proposals for formal theories of space in which spatial regions are primitives, rather than constructions from sets of more fundamental points. One motivation for some of…

### Spatial reasoning with RCC8 and connectedness constraints in Euclidean spaces

- MathematicsArtif. Intell.
- 2014

### On Mereologies in Computing Science

- PhilosophyReflections on the Work of C. A. R. Hoare
- 2010

A formal model of a large class of mereologies, with simple entities modelled as parts and their relations by connectors is given, and it is shown that class applies to a wide variety of societal infrastructure component domains.

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