Journal of Philosophical Logic

, Volume 44, Issue 3, pp 309–319 | Cite as

Mally’s Deontic Logic: Reducibility and Semantics

  • Gert-Jan C. LokhorstEmail author


We discuss three aspects of the intuitionistic reformulation of Mally’s deontic logic that was recently proposed (Journal of Philosophical Logic 42, 635–641, (2013)). First, this reformulation is more similar to Standard Deontic Logic than appears at first sight: like Standard Deontic Logic, it is Kanger reducible and Anderson reducible to alethic logic and it has a semantical interpretation that can be read in deontic terms. Second, this reformulation has an extension that provides 100% of the theorems stated by Mally himself (and that does not provide O AA, which Mally himself did not state either). Third, it is interesting to view Mally’s original deontic logic as an extension of this reformulation.


Deontic logic Intuitionistic logic 



The author is grateful to John F. Horty, whose question whether intuitionistic double negation is really a deontic modality (at the Formal Ethics conference, LMU Munich, Oct 11, 2012) provoked this paper.


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Section of Philosophy Faculty of Technology, Policy and ManagementDelft University of TechnologyDelftThe Netherlands

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