Foundations for a Formalism of Nearness

The preposition at from a spatial language, cognition, and information systems perspective

“…However, at has not been discussed (perhaps has not been perceived) in the GIScience literature as a qualitative distance relationship (Hernández, Clementini & Di Felice 1995). The qualitative distance relationship closest to the meaning of at is 'nearness' (Brennan & Martin 2002, Worboys 2001. But even if nearness is seen as an abstraction from quantity of distance in such accounts, clearly we still need to distinguish the meaning of at from the meaning of near, because unlike at, near cannot represent the full range of topologically dependent relationships demonstrated above (it cannot include spatial arrays of meeting or containing), because the distance-related dimension of meaning encoded in near is greater than the 'near zero length' vector at is assigned in formal semantics.…”

“…With such a set of contrasting locations in mind, the meaning of 'at a location A' is limited to locations which are closer to A than to B or to any other alternative location to A in the given contrast set -assuming that the contrast set forms part of the context of the conversation. Taking up an argument by Brennan & Martin (2002), at some level at therefore reflects not a binary absolute proximity relation (cf. 'near A'), but a ternary comparative proximity relation: 'X is nearer to A than any other alternative(s) of the contrast set'.…”

Vague Spatio-Thematic Query Processing: A Qualitative Approach to Spatial Closeness

“…Brennan and Martin (2002) introduce a qualitative representation of spatial proximity that accounts for absolute binary nearness relations. The formalism is based on the notion of perceived points, called sites, in a point‐based universe.…”

“…The approach introduced by Brennan and Martin (2002) and that presented here have in common that the qualitative description of nearness is based on a qualitative representation of distance: in their case Voronoi diagrams transform (quantitative) distances into a network of (qualitative) topological relations. This is different from all other approaches discussed in this article, where a mapping mechanism between qualitative and metric distance measures is established (or implied).…”

Positioning Locality Using Cognitive Directions Based on Indoor Landmark Reference System

“…The conceptual function between the membership degree of “near” and the distance between objects is defined in [ 10 ], but no related practical application is discussed. In computational geometry, the near relation can be represented by Voronoi diagrams [ 13 ]. Gong [ 12 , 14 ] proposed a mixed-selection probability function that was based on Euclidean distance and Voronoi stolen area to model near relations.…”