The Unreasonable Effectiveness of Bitstrings in Logical Geometry

Chapter

Abstract

This paper presents a unified account of bitstrings—i.e. sequences of bits (0/1) that serve as compact semantic representations—for the analysis of Aristotelian relations and provides an overview of their effectiveness in three key areas of the Logical Geometry research programme. As for logical effectiveness, bitstrings allow a precise and positive characterisation of the notion of logical independence or unconnectedness, as well as a straightforward computation—in terms of bitstring length and level—of the number and type of Aristotelian relations that a particular formula may enter into. As for diagrammatic effectiveness, bitstrings play a crucial role in studying the subdiagrams of the Aristotelian rhombic dodecahedron, and different types of Aristotelian hexagons turn out to require bitstrings of different lengths. The linguistic and cognitive effectiveness of bitstring analysis relates to the scalar structure underlying the bitstrings, and to the difference between linear and non-linear bitstrings.

Keywords

Aristotelian diagram Bitstrings Cognitive effectiveness Diagrammatic effectiveness Linguistic effectiveness Logical effectiveness Logical geometry Unconnectedness 

Mathematics Subject Classification (2000)

Primary 03G05 68T30; Secondary 03B65 06A07 00A66 97C30 

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Research Group on Formal and Computational LinguisticsKU LeuvenLeuvenBelgium
  2. 2.Center for Logic and Analytic PhilosophyKU LeuvenLeuvenBelgium

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