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On the modal interpretation of the connective of realisation

On the modal interpretation of the connective of realisation The connective of realisation associates propositions with names of contexts, at which they are said to be realised. Realisation is usually understood as relativised truth-connective, thus under most accounts it distributes over all Boolean connectives. Nonetheless, there are good reasons to consider weaker kinds of realisation, which lack some distributive laws. Three kinds of semantics for such weak realisation were provided: many-valued, set-theoretic and relational. The paper addresses the problem of Jarmużek's interpretation of the connective of realisation in relational models. It is argued that Jarmużek truth condition for the connective of realisation is tantamount to imposing symmetry on the relation of accessibility in a model. Moreover, a simplified semantics as well as axiom system for Jarmużek system are presented. Finally, a unification with Tkaczyk's – most general -- results is provided by proving completeness result for the axiom system with respect to Tkaczyk-style set-theoretic semantics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

On the modal interpretation of the connective of realisation

Karczewska, A. M.
Journal of Applied Non-Classical Logics , Volume 31 (3-4): 13 – Oct 2, 2021
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On the modal interpretation of the connective of realisation

Abstract

The connective of realisation associates propositions with names of contexts, at which they are said to be realised. Realisation is usually understood as relativised truth-connective, thus under most accounts it distributes over all Boolean connectives. Nonetheless, there are good reasons to consider weaker kinds of realisation, which lack some distributive laws. Three kinds of semantics for such weak realisation were provided: many-valued, set-theoretic and relational. The paper addresses...
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Publisher
Taylor & Francis
Copyright
© 2021 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2021.1982552
Publisher site
See Article on Publisher Site

Abstract

The connective of realisation associates propositions with names of contexts, at which they are said to be realised. Realisation is usually understood as relativised truth-connective, thus under most accounts it distributes over all Boolean connectives. Nonetheless, there are good reasons to consider weaker kinds of realisation, which lack some distributive laws. Three kinds of semantics for such weak realisation were provided: many-valued, set-theoretic and relational. The paper addresses the problem of Jarmużek's interpretation of the connective of realisation in relational models. It is argued that Jarmużek truth condition for the connective of realisation is tantamount to imposing symmetry on the relation of accessibility in a model. Moreover, a simplified semantics as well as axiom system for Jarmużek system are presented. Finally, a unification with Tkaczyk's – most general -- results is provided by proving completeness result for the axiom system with respect to Tkaczyk-style set-theoretic semantics.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Oct 2, 2021

Keywords: Positional logics; topological logics; connective of realisation

References

  • Completeness of minimal positional calculus
  • Podstawy analizy metodologicznej kanonów Milla
  • Logiki wielowartościowe a formalizacja funkcji intensjonalnych (Many-valued logics and formalization of intensional functions)
  • Topological logic
  • Negation in weak positional calculi
  • Distribution laws in weak positional logics
  • Jerzy Łoś positional calculus and the origin of temporal logic