A Theory of Granular Partitions

Abstract

-There are some who defend a view of vagueness according to which there are intrinsically vague objects or attributes in reality. Here, in contrast, we defend a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts on the one hand and correlated portions of reality on the other. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches.

Modeling Surface Hydrology Concepts with Endurance and Perdurance

“…Through the participate relation between endurants and perdurants, it is possible to identify the functions of an endurant in monitoring water flow on the land surface. One interesting issue that is not handled in this work is the issue of granularity [3]. Some dependent endurants identified for catchment, such as the two routing coefficients in a sub-model of HEC-HMS, indicate the intention of describing overland flow and channel flow behavior in the model.…”

A Top-Level Categorization of Types of Granularity

“…The notions of similarity, equivalence, and indistinguishability relations have been well investigated with set-based approaches (Bittner & Stell, 2003;Chen & Yao, 2006;Hata & Mukaidono, 1999;Keet, 2007a;Mencar et al, 2007;Peters et al, 2002;Skowron & Peters, 2003;Yao, 2004). However, this set-based approach has issues that can be better addressed with mereology proper (Abelló et al, 2006;Bittner & Smith, 2003;Keet, 2008a). The research programme of rough mereology (see, e.g., Polkowski (2006); Polkowski & Semeniuk-Polkowska (2008) for recent results) has, from an ontological (Varzi, 2004;Keet & Artale, 2008) and logical (Pontow & Schubert, 2006) perspective, a comparatively weak mereology component, because it is tightly coupled with the set-based approach and remains close to Lesniewski's pioneering work without considering newer mereological theories.…”

“…Also, they have specified a large set of one-off functions and data manipulation operators only at the design or implementation layer, requiring a re-coding of functions, such as for calendar hierarchies and products sold; compare e.g., GMD, MSD, MADS, and MultiDimER (Kamble, 2004;Fagin et al, 2005;Parent et al, 2006a;Malinowski & Zimányi, 2006), or see Euzenat & Montanari (2005) for an overview on theories of and functions for time granularity and Ning et al (2002) for a particular example. Hobbs (1985) has introduced several core components of granularity and Bittner & Smith (2003) have developed an ontologically-motivated formal "theory of granular partitions" (TGP) based on mereology. The TGP is relatively comprehensive and useful for granular levels, but it is limited to mereology, does not address the types of aggregation commonly used with data mining and conceptual data modelling, has no functions, no mechanism to deal with multiple granulation hierarchies for different perspectives, and does not allow for the kind of granularity and abstraction commonly used in biology or Mani's (1998) folding operations in linguistics.…”

Toward a Realistic Science of Environments

“…In principle, therefore, all members of a family of mutually conflicting 'perceptual spaces' may well turn out to be compatible after all, if they can be interpreted as expressing distinct partitions, for example partitions on different levels of granularity, of one and the same reality. (Bittner and Smith 2003) In this way the second motive for representationalism may be resisted, too, and therewith also for a representationalist reading of Gibson. In full conformity with the realist perspective, different languages, different theories, and different families of organisms are able to generate their own precisely fitting partitions of one single reality.…”