LP, K3, and FDE as Substructural Logics

In Arazim Pavel & Lávička Tomáš, The Logica Yearbook 2016. College Publications (2017)
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Abstract

Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”

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Lionel Shapiro
University of Connecticut

References found in this work

Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Groningen: North-Holland.
An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - New York: Cambridge University Press.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Entailment: The Logic of Relevance and Necessity. - 1975 - Studia Logica 54 (2):261-266.

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