Logic of left variable inclusion and Plonka sums of matrices

Abstract

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

to appear in Archive for Mathematical Logic

References in corpus (2)

• Dualities for Plonka sums
• Stone-type representations and dualities for varieties of bisemilattices

Cited by in corpus (5)

• Group representation for even and odd involutive commutative residuated chains
• Restricted Rules of Inference and Paraconsistency
• Monadicity of Non-deterministic Logical Matrices is Undecidable
• Finite Hilbert systems for Weak Kleene logics
• Płonka Adjunction