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arXiv · 1804.08897

Logic of left variable inclusion and Plonka sums of matrices

Stefano Bonzio·Tommaso Moraschini·Michele Pra Baldi
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Abstract

The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic $\vdash$. It turns out that the algebraic counterpart of the variable inclusion companion of a given logic $\vdash$ is obtained by constructing the Plonka sum of the matrix models of $\vdash$. This association allows to obtain a Hilbert-style axiomatization of the logics of variable inclusion and to describe the structure of their reduced models.

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Stefano Bonzio, Tommaso Moraschini, Michele Pra Baldi. 2018-04-24. Logic of left variable inclusion and Plonka sums of matrices. https://doi.org/10.1007/s00153-020-00727-6

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