Logica Universalis

, Volume 10, Issue 2, pp 233–292

Metalogical Decorations of Logical Diagrams

Article

DOI: 10.1007/s11787-015-0136-6

Cite this article as:
Demey, L. & Smessaert, H. Log. Univers. (2016) 10: 233. doi:10.1007/s11787-015-0136-6

Abstract

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of (sub)contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams (viz. Aristotelian and duality diagrams) and four kinds of metalogical decorations (viz. those based on the opposition, implication, Aristotelian and duality relations).

Keywords

Aristotelian diagram duality diagram metalogic opposition geometry implication geometry contrariety 

Mathematics Subject Classification

Primary 03A10 03B45 Secondary 03B65 03B80 

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Center for Logic and Analytic Philosophy, KU LeuvenLeuvenBelgium
  2. 2.Department of Linguistics, KU LeuvenLeuvenBelgium