Elementary Polyhedral Mereotopology

Pratt-Hartmann, Ian; Schoop, Dominik

doi:10.1023/a:1020184007550

Cited by 6 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• all non-empty regular closed subsets of R n [6] • all open polygonal (polyhedral, etc) subsets of R n [13,14,15] In these interpretations, it is usual to interpret the predicates P and C as standing for the following relations:…”

mentioning

confidence: 99%

Mereology and the Sciences

Calosi¹,

Graziani²

2014

Synthese Library

View full text Add to dashboard Cite

Whereas mereology, in the strict sense, is concerned solely with the partwhole relation, mereotopology extends mereology by including also the notion of connection, enabling one to distinguish, for example, between internal and peripheral parts, and between contact and separation. Mereotopology has been developed particularly within the Qualitative Spatial Reasoning research community, where it has been applied to, amongst other areas, geographical information science and image analysis. Most research in mereotopology has assumed that the entities being studied may be subdivided without limit, but a number of researchers have investigated mereotopological structures based on discrete spaces in which entities are built up from atomic elements that are not themselves subdivisible. This chapter presents an introductory treatment of mereotopology and its discrete variant, and provides references for readers interested in pursuing this subject in further detail. From Mereology to MereotopologyMereology, as the theory of parts and wholes, leads to a set of five jointly exhaustive and pairwise disjoint (JEPD) relations that may hold between any pair of entities X and Y that come under its purview, namely X is a proper part of Y PP(x, y) X coincides with Y EQ(x, y) X partially overlaps Y PO(x, y) X contains Y as a proper part PPI(x, y) X is disjoint from Y DR(x, y)

show abstract

mentioning

confidence: 99%

Mereology and the Sciences

Calosi¹,

Graziani²

2014

Synthese Library

View full text Add to dashboard Cite

show abstract

“…In the first case, one focuses on the interdefinability of primitive relations assumed in the theories to prove the equivalence of their axiomatics, while in the second case, one compares (classes of) models of these theories. Systematic analyses of these kinds have been developed on mereotopologies: Casati & Varzi (1999), Simons (1987), and Masolo & Vieu (1999) consider the syntactic level, while Biacino & Gerla (1991, Asher & Vieu (1995), Pratt-Hartmann & Schoop (1998, 2002, Roeper (1997), and Stell (2000) focus on the semantic level.…”

mentioning

confidence: 99%

Full Mereogeometries

Borgo¹,

Masolo

2010

The Review of Symbolic Logic

View full text Add to dashboard Cite

We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to isolate comparable models for each theory. Relying on the chosen interpretations, we introduce the notion of environment structure, that is, a minimal structure that contains a (sub)structure for each theory. In particular, in the case of mereogeometries, the domain of an environment structure is composed of particular subsets of Rn. The comparison of mereogeometrical theories within these environment structures shows dependencies among primitives and provides (relative) definitional equivalences. With one exception, we show that all the theories considered are equivalent in these environment structures.

show abstract

First-Order Mereotopology

Pratt-Hartmann

2007

Handbook of Spatial Logics

View full text Add to dashboard Cite

Elementary Polyhedral Mereotopology

Cited by 6 publications

References 11 publications

Mereology and the Sciences

Mereology and the Sciences

Full Mereogeometries

First-Order Mereotopology

Contact Info

Product

Resources

About