Logica Universalis 9 (1):47-92 (2015)

Authors
Clayton Peterson
Université de Montréal
Abstract
This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspective of category theory. While Chisholm’s paradox hints at the need of dyadic deontic logic by showing that monadic deontic logics are not able to adequately model conditional obligations and contrary-to-duties, other arguments can be objected to dyadic approaches in favor of non-monotonic foundations. We show that all these objections can be answered at one fell swoop by modeling conditional obligations within a deductive system defined as an instance of a symmetric monoidal closed category. Using category theory as a foundational framework for logic, we show that it is possible to model conditional normative reasoning and conflicting obligations within a monadic approach without adding further operators or considering deontic conditionals as primitive
Keywords Conditional obligations  factual detachment  augmentation  deontic explosion  normative consistency  categorical logic  deontic logic  dyadic deontic logic  non-monotonic logic
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DOI 10.1007/s11787-014-0111-7
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References found in this work BETA

Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
Input/Output Logics.David Makinson & Leendert van der Torre - 2000 - Journal of Philosophical Logic 29 (4):383-408.
Constraints for Input/Output Logics.David Makinson & Leendert van der Torre - 2001 - Journal of Philosophical Logic 30 (2):155 - 185.
Input/Output Logics.David Makinson & Leendert Van Der Torre - 2000 - Journal of Philosophical Logic 29 (4):383 - 408.

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Citations of this work BETA

A Comparison Between Monoidal and Substructural Logics.Clayton Peterson - 2016 - Journal of Applied Non-Classical Logics 26 (2):126-159.
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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