Open Reading and Free Choice Permission : A Perspective in Substructural Logics

Title data

Roy, Olivier ; Dong, Huimin ; Gratzl, Norbert:
Open Reading and Free Choice Permission : A Perspective in Substructural Logics.
In: Liao, Beishui (ed.): Dynamics, Uncertainty and Reasoning. - Singapore : Springer , 2019 . - (Logic in Asia )
ISBN 978-981-13-7790-7

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Abstract in another language

This paper proposes a new solution to the well-known Free Choice Permission Paradoxes (Barker 2010; Hansson 2014), combining ideas from substructural logics and non-monotonic reasoning. Free choice permission is intuitively understood as “if it is permitted to do or then it is permitted to do and it is permitted to do.” Yet, one of its logically equivalent forms allows the following inference which seems unacceptable: if it is permitted to order a vegetarian lunch then it is permitted to order a vegetarian lunch and not pay for it (Hansson 2013). The challenge for a logic of free choice permission is to exclude such counterintuitive consequences while not giving up too much deductive power. We suggest that the right way to do so is using a family of substructural logics augmented with a principle borrowed from non-monotonic reasoning. This follows up on a proposal made in Anglberger et al. (2014).