Studia Logica 66 (1):5-40 (2000)

Authors
Jon Michael Dunn
PhD: University of Pittsburgh; Last affiliation: Indiana University, Bloomington
Abstract
This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson 's "constructible falsity"
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/a:1026740726955
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References found in this work BETA

Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.
In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.

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Citations of this work BETA

HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.

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