LIRa Session: Johannes Korbmacher

Speaker: Johannes Korbmacher

Date and Time: Thursday, November 15th 2018, 17:00-18:30

Venue: ILLC Seminar Room F1.15, Science Park 107.

Title: The Logic of Free Choice Permission.

Abstract. Building on a suggestion by Kit Fine, we describe a logic of permission using exact truthmaker semantics. The only logical principle for permission in the system is Free Choice Permission (FCP):

P (φ ∨ ψ)  P φ ∧ P ψ.

By drawing on the resources of exact truthmaker semantics, we avoid the standard problems associated with (FCP).

Our logic is a positive propositional deontic logic, i.e. it neither has negation nor any kind of implication. The connectives are simply ∨, ∧ and the permission operator P. Notably, the system has no theorems. We give a sound and complete axiomatization in terms of deducibility statements φ ⊢ ψ.

We then study extensions of the system with certain plausible principles for permission. In particular, we’ll determine semantic conditions that are equivalent to the validity of Pφ ∧ Pψ  P(φ ∨ ψ) and of P (φ ∧ ψ)  P φ ∧ P ψ.

(This is a joint work with Albert Anglberger.)