Notre Dame Journal of Formal Logic

Generalizing the Depth Relevance Condition: Deep Relevant Logics Not Included in R-Mingle

Gemma Robles and José M. Méndez

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Abstract

Brady has shown how to define a class of deep relevant logics from Meyer’s crystal lattice CL. The aim of this paper is to generalize Brady’s result by showing how to define a class of deep relevant logics from each weak relevant matrix (weak relevant matrices only verify logics with the variable-sharing property). A class of deep relevant logics not included in R-Mingle is defined.

Article information

Source
Notre Dame J. Formal Logic, Volume 55, Number 1 (2014), 107-127.

Dates
First available in Project Euclid: 20 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1390246442

Digital Object Identifier
doi:10.1215/00294527-1960461

Mathematical Reviews number (MathSciNet)
MR3161416

Zentralblatt MATH identifier
06279845

Subjects
Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Keywords
deep relevant logics relevant logics weak relevant matrices logical matrices

Citation

Robles, Gemma; Méndez, José M. Generalizing the Depth Relevance Condition: Deep Relevant Logics Not Included in R-Mingle. Notre Dame J. Formal Logic 55 (2014), no. 1, 107--127. doi:10.1215/00294527-1960461. https://projecteuclid.org/euclid.ndjfl/1390246442


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References

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