Tracking reasons with extensions of relevant logics

Logic Journal of the IGPL 27 (4):543-569 (2019)
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Abstract

In relevant logics, necessary truths need not imply each other. In justification logic, necessary truths need not all be justified by the same reason. There is an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way. In this paper, I will show how to extend relevant logics with some of the basic operators of justification logic in order to track justifications or reasons. I will define and study three kinds of frames for these logics. For the first kind of frame, I show soundness and highlight a difficulty in proving completeness. This motivates two alternative kinds of frames, with respect to which completeness results are obtained. Axioms to strengthen the justification logic portions of these logics are considered. I close by developing an analogy between the dot operator of justification logic and theory fusion in relevant logics.

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Shawn Standefer
National Taiwan University

Citations of this work

Relevance logic.Edwin Mares - 2008 - Stanford Encyclopedia of Philosophy.
Neighbourhood Semantics for Quantified Relevant Logics.Andrew Tedder & Nicholas Ferenz - 2022 - Journal of Philosophical Logic 51 (3):457-484.
A Substructural Approach to Explicit Modal Logic.Shawn Standefer - 2023 - Journal of Logic, Language and Information 32 (2):333–362.
Neighbourhood Semantics for Modal Relevant Logics.Nicholas Ferenz & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (1):145-181.

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References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
The Connectives.Lloyd Humberstone - 2011 - MIT Press. Edited by Lloyd Humberstone.
Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.

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