On the Logical Geometry of Geometric Angles

In this paper we provide an analysis of the logical relations within the conceptual or lexical field of angles in 2D geometry. The basic tripartition into acute/right/obtuse angles is extended in two steps: first zero and straight angles are added, and secondly reflex and full angles are added, in b...

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Bibliographic Details
Published in:Logica universalis 2022-12, Vol.16 (4), p.581-601
Main Authors: Smessaert, Hans, Demey, Lorenz
Format: Article
Language:English
Subjects:
Angles (geometry)
Computer Science
Logic
Mathematics
Mathematics and Statistics
Semantics
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Summary:In this paper we provide an analysis of the logical relations within the conceptual or lexical field of angles in 2D geometry. The basic tripartition into acute/right/obtuse angles is extended in two steps: first zero and straight angles are added, and secondly reflex and full angles are added, in both cases extending the logical space of angles. Within the framework of logical geometry, the resulting partitions of these logical spaces yield bitstring semantics of increasing complexity. These bitstring analyses allow a straightforward account of the Aristotelian relations between angular concepts. In addition, also relational concepts such as complementary and supplementary angles receive a natural bitstring analysis.
ISSN:1661-8297
1661-8300
DOI:10.1007/s11787-022-00315-7