VSL 2014: VIENNA SUMMER OF LOGIC 2014

On Affine Logic and Łukasiewicz Logic

Authors: Rob Arthan and Paulo Oliva

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Title:On Affine Logic and Łukasiewicz Logic
Authors:Rob Arthan and Paulo Oliva
Proceedings:GSB 2014 Proceedings
Editors: Roman Kuznets and George Metcalfe
Keywords:Lukasiewicz logic, Affine logic, Negative translation, Double negation translation
Abstract:

ABSTRACT. We report on a study of intutionistic fragments of classical Lukasiewicz logic. We present, in a structured human readable form, syntactic proofs of a number of important formulas originally found with the assistance of the Prover9 automated theorem prover. The identities include homomorphism properties that we put to work in an analysis of the double negation translations of Kolmogorov, Goedel, Gentzen and Glivenko.

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