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On Sahlqvist Formulas in Relevant Logic.

Guillermo Badia1

  • 1Department of Knowledge-Based Mathematical Systems, Johannes Kepler Universität, Linz, Austria.

Journal of Philosophical Logic
|August 14, 2018
PubMed
Summary
This summary is machine-generated.

This study defines a Sahlqvist fragment for relevant logic, proving that Sahlqvist definable frame classes in Routley-Meyer semantics are elementary. However, not all relevant formulas define elementary classes of Routley-Meyer frames.

Keywords:
Correspondence theoryFrame definabilityRelevant logicRoutley-Meyer semanticsSahlqvist’s correspondence

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Area of Science:

  • Logic
  • Formal Semantics
  • Mathematical Logic

Background:

  • Relevant logic is a key area in non-classical logic.
  • Routley-Meyer semantics provides a framework for analyzing relevant logics.
  • Sahlqvist formulas have important properties related to definability and decidability.

Purpose of the Study:

  • To define a Sahlqvist fragment for relevant logic.
  • To investigate the relationship between Sahlqvist definability and elementary classes of frames in Routley-Meyer semantics.
  • To explore limitations of Sahlqvist formulas in capturing all definable frame classes.

Main Methods:

  • Definition of a Sahlqvist fragment tailored for relevant logic.
  • Application of the Sahlqvist-van Benthem algorithm to determine first-order properties.
  • Analysis of classes of frames within the Routley-Meyer semantics.

Main Results:

  • Established that Sahlqvist definable classes of Routley-Meyer frames are elementary.
  • Demonstrated that these elementary classes correspond to specific first-order properties.
  • Showcased that certain relevant formulas define non-elementary classes of frames.

Conclusions:

  • Sahlqvist formulas provide a powerful tool for characterizing elementary classes of frames in relevant logic semantics.
  • The expressiveness of relevant formulas is not fully captured by the elementary classes definable via Sahlqvist formulas.
  • This research advances the understanding of the expressive power and limitations of Sahlqvist formulas in non-classical logics.