Olivier Roy-Turgeon

We revisit a recent puzzle about common knowledge, the ``sailboat" case (Lederman, 2018), and argue that Lewisian common knowledge allows us to reconcile the pre-theoretical intuition that certain facts are ``public" in such situations, while these facts cannot be common knowledge in the classical, iterative sense. The crux of the argument is to understand Lewisian common knowledge as an account of what it means for an event to be public. We first formulate this argument informally to clarify its philosophical commitment and then propose one way to capture it formally in epistemic-plausibility models. Taken together, we take the philosophical and the formal arguments as providing evidence that Lewisian common knowledge is a plausible account of what it means for an event to be public.

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).

Epistemic game theory has shown the importance of informational contexts to understand strategic interaction. We propose a general framework to analyze how such contexts may arise. The idea is to view informational contexts as the fixed points of iterated, rational responses to incoming information about the agents’ possible choices. We discuss conditions under which such fixed points may exist. In the process, we generalize existing rules for information updates used in the dynamic epistemic logic literature. We then apply this framework to weak dominance. Our analysis provides a new perspective on a well known problem with the epistemic characterization of iterated removal of weakly dominated strategies.