Abstract

This paper proposes a new solution to the well-known Free Choice Permission Paradoxes (Barker 2010; Hansson 2013; Xin and Dong 2014), combining ideas from substructural logics and non-monotonic reasoning. Free choice permission is intuitively understood as “if it is permitted to do \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} then it is permitted to do \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and it is permitted to do \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}.” 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).