Another plan for negation

Australasian Journal of Logic 16 (5):159 (2019)

Nissim Francez
Technion, Israel Institute of Technology
The paper presents a plan for negation, proposing a paradigm shift from the Australian plan for negation, leading to a family of contra-classical logics. The two main ideas are the following: Instead of shifting points of evaluation, shift the evaluated formula. Introduce an incompatibility set for every atomic formula, extended to any compound formula, and impose the condition on valuations that a formula evaluates to true iff all the formulas in its incompatibility set evaluate to false. Thus, atomic sentences are not independent in their truth-values. The resulting negation, in addition to excluding the negated formula, provides a positive alternative to the negated formula. I also present a sound and complete natural deduction proof systems for those logics. In addition, the kind of negation considered in this paper is shown to provide an innovative notion of grounding negation.
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DOI 10.26686/ajl.v16i5.5190
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References found in this work BETA

Guide to Ground.Kit Fine - 2012 - In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical Grounding. Cambridge University Press. pp. 37--80.
An Introduction to Grounding.Kelly Trogdon - 2013 - In Miguel Hoeltje, Benjamin Schnieder & Alex Steinberg (eds.), Varieties of Dependence. Munich, Germany: Philosophia Verlag. pp. 97-122.
Logical Grounds.Fabrice Correia - 2013 - Review of Symbolic Logic (1):1-29.
Negation on the Australian Plan.Franz Berto & Greg Restall - 2019 - Journal of Philosophical Logic 1:1-26.

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