A decision-tree inspired semantics of a logic of conditional imperatives and permissives

(Logic, )

ecently, Evans et al. introduced a logic of coditional imperatives and permissives. Conditional imperatives roughly amount to expressions of the kind ``If you are doing A, you must do something from B'', for sets of actions A und B. Similarly, conditional permissives could be rephrased as ``If you are doing A, feel free to do something from B''. Whilst Evans et al. develop their system with Kant's theoretical philosophy as an application in mind, one can easily imagine other deontic contexts where such rules are relevant. Imagine an agent at the grocery store, where they would be subject to rules such as ``You might enter the grocery store.'' and ``If you enter the grocery store, you have to mask your face'' nowadays.

In the light of these applications, the task of finding semantics and logics for such systems appears interesting. Evans et al. introduce two options for a semantics. In this talk, I want to introduce a third option, which formalises the idea of deriving all possible courses of action by a decision tree. Technically speaking, redundance in semantics is desirable as different claims might appear easier to proof in one system or the other.

Roughly, we follow this idea: The agent, already performing acts A, and subject to a set of rules R first considers which rules of R are applicable. If there is at least one such rule r, they opt for a course of action A' in line with the chosen rule. Then, the procedure is repeated recursively for A' and R\{r} until no applicable rules are left. In my talk, I give the exact formal definitions of this idea, followed by an overview of how equivalence to the second semantics of Evans et al. can be established.

Reference:

Evans, R., Sergot, M. & Stephenson, A. Formalizing Kant's Rules. J Philos Logic 49, 613--680 (2020). https://doi.org/10.1007/s10992-019-09531-x

Chair: Yannick Kohl

Time: 12:00-12:30, 11 September 2021 (Saturday)

Location: SR 1.006

Remark: (Online Talk)

Fabian Heimann

(University of Göttingen, Germany)

I am a Phd student in Mathematics based in Göttingen. Apart from applied math, my research focuses mostly on philosophical logic. More specifically, I worked on a puzzle in languages with several modal operators and Kripkean theories of probability and truth, before delving into the systems of deontic logic described in my abstract. Methodologically, I like to formalise results in the proof machine Isabelle for technical convenience.

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