The Search for Symmetry in Hohfeldian Modalities

Matteo Pascucci, Giovanni Sileno

Research output: Contribution to Book/Report typesConference contributionpeer-review

Abstract (may include machine translation)

In this work we provide an analysis of some issues arising with geometrical representations of a family of deontic and potestative relations that can be classified as Hohfeldian modalities, traditionally illustrated on two diagrams, the Hohfeldian squares. Our main target is the lack of symmetry to be found in various formal accounts by drawing analogies with the square of opposition for alethic modalities. We argue that one should rather rely on an analogy with the alethic hexagon of opposition and exploit the notions of contingency and absoluteness in order to restore the symmetry of Hohfeldian modalities in accordance to the diagrams presented by Hohfeld. Interestingly, the investigation unveils three potestative squares defined at different levels of granularity (force, outcome and change) and allows us to further elaborate on the connections between deontic and potestative relations.

Original languageEnglish
Title of host publicationDiagrammatic Representation and Inference - 12th International Conference, Diagrams 2021, Proceedings
EditorsAmrita Basu, Gem Stapleton, Sven Linker, Catherine Legg, Emmanuel Manalo, Petrucio Viana
PublisherSpringer Science and Business Media Deutschland GmbH
Pages87-102
Number of pages16
ISBN (Print)9783030860615
DOIs
StatePublished - 2021
Externally publishedYes
Event12th International Conference on the Theory and Application of Diagrams, Diagrams 2021 - Virtual, Online
Duration: 28 Sep 202130 Sep 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12909 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th International Conference on the Theory and Application of Diagrams, Diagrams 2021
CityVirtual, Online
Period28/09/2130/09/21

Keywords

  • Deontic relations
  • Hohfeldian modalities
  • Hohfeld’s cube
  • Modal hexagon of opposition
  • Potestative relations
  • Power
  • Symmetry

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