Authors
Clayton Peterson
Université de Montréal
Abstract
Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The purpose of the present paper is to address this issue and highlight the differences between these two approaches. We argue that monoidal logics provide a more flexible foundational framework that enables a finer analysis of the relationship between negation and other logical connectives. We show that the elimination of double negation is independent from the de Morgan dualities, that monoidal deductive systems are not necessarily weakly distributive and that deduc...
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DOI 10.1080/11663081.2016.1179528
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References found in this work BETA

Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
A Survey of Abstract Algebraic Logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.

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Citations of this work BETA

Studies in the Logic of K -Onfirmation.Clayton Peterson - 2019 - Philosophical Studies 176 (2):437-471.
Monoidal Logics: Completeness and Classical Systems.Clayton Peterson - 2019 - Journal of Applied Non-Classical Logics 29 (2):121-151.

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