Abstract
We approach the semantics of prepositions from the perspective of conceptual spaces. Focusing on purely spatial locative and directional prepositions, we analyze both types of prepositions in terms of polar coordinates instead of Cartesian coordinates. This makes it possible to demonstrate that the property of convexity holds quite generally in the domain of prepositions of location and direction, supporting the important role that this property plays in conceptual spaces.
Highlights
Prepositions are a limited class of words, but with a wide range of meanings and uses, even if we consider only locative prepositions in one language, like English in, near, over or behind (Lindstromberg 2010). (1) a
If we focus on simple paths that are defined as mappings from the interval [0,1] to points x, θ in one plane, the following general definition adopts the polar geometry for paths:12 (28) Let pa(i) and pc(i), where i ∈ [0,1], be two paths mapping onto xa(i), θa(i) and xc(i), θc(i) respectively
The main topic of this paper has been the use of geometric notions to describe the semantics of locative and directional prepositions
Summary
We turn from locative prepositions to directional prepositions, which are used to describe how a trajector is moving with respect to a landmark:. If a trajector is moving or if it is extended in shape, we need the notion of a path, i.e. a directed curve (see for instance Jackendoff 1983; Talmy 2000; Eschenbach et al 2000; Zwarts 2005; Kracht 2008, and many others). In the sequel we make the assumption that the path is simple, that is, it does not cross itself. This can be defined by saying that for all i, j ∈ [0, 1], such that i = j, p(i) = p( j). All the points of a path are represented in terms of polar coordinates taken from S.
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