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Vague distance predicates

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Abstract

A formal theory of vague distance predicates is presented which combines a crisp region-based geometry with a theory of vague size predicates in a supervaluation-based formal framework. In the object language of the axiomatic theory, logical and semantic properties of vague distance predicates that are context- and domain-independent are formalized. Context and domain-dependent aspects are addressed in the meta-language of the theory by incorporating context- and domain-specific restrictions on the canonical interpretations. This allows to relate the ontological and qualitative analysis in the object language to numeric values as they are commonly used in scientific discourses.

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Notes

  1. The notations U and S are adopted from [2].

  2. The Lebesgue measure is a formalization of the intuitive notion of the length of d if d is a regular subset of R 1. ∥d∥ is the area of d if d a regular subset of R 2 and ∥d∥ is the volume of d if d a regular subset of R 3.

  3. The operator I corresponds to Fine’s indefiniteness operator [23] and the operator D corresponds to Pinkal’s definiteness operator [35].

  4. Consider the distance predicates {C,c,M,f,F} between points of [24] and [28]. Roughly, for regions of the same size, S C l corresponds to C, SN corresponds to c, MA corresponds to M, and FA corresponds to the disjunction of f and F. Note, however that the definitions given here are for regions rather than for points and take the size of the regions into account. The predicate S C l roughly corresponds to the predicate ‘near’ of [40].

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  1. Departments of Philosophy, Geography State University of New York at Buffalo, Buffalo, NY, USA

    Thomas Bittner

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Bittner, T. Vague distance predicates. Geoinformatica 21, 209–229 (2017). https://doi.org/10.1007/s10707-016-0285-7

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