Notre Dame Journal of Formal Logic

A General Characterization of the Variable-Sharing Property by Means of Logical Matrices

José M. Méndez and Gemma Robles

Abstract

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. In this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided.

Article information

Source
Notre Dame J. Formal Logic, Volume 53, Number 2 (2012), 223-244.

Dates
First available in Project Euclid: 9 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1336588252

Digital Object Identifier
doi:10.1215/00294527-1715707

Mathematical Reviews number (MathSciNet)
MR2925279

Zentralblatt MATH identifier
1254.03041

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

Keywords
logical matrices variable-sharing property relevant logics

Citation

Robles, Gemma; Méndez, José M. A General Characterization of the Variable-Sharing Property by Means of Logical Matrices. Notre Dame J. Formal Logic 53 (2012), no. 2, 223--244. doi:10.1215/00294527-1715707. https://projecteuclid.org/euclid.ndjfl/1336588252


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References

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