Toward a Linguistic Interpretation of Deontic Paradoxes A Beth-Reichenbach semantics approach for a new analysis of the miners scenario Dov Gabbay 1,2 , Livio Robaldo 3 , Xin Sun 2 , Leendert van der Torre 2 , Zohreh Baniasadi 2 1 Department of Computer Science, King’s College London, 2 Faculty of Science, Technology and Communication, University of Luxembourg, 3 Department of Computer Science, University of Turin, dov.gabbay@kcl.ac.uk, robaldo@di.unito.it, xin.sun@uni.lu, leon.vandertorre@uni.lu, zohreh.baniasadi.001@student.uni.lu Abstract. A linguistic analysis of deontic paradoxes can be used to further de- velop deontic logic. In this paper we provide a Beth-Reichenbach semantics to analyze deontic paradoxes, and we illustrate it on the single agent decision prob- lem of the miners scenario. We also introduce extensions with reactive arrows and actions, which can be used to give a linguistic interpretation of multi-agent dialogues. 1 Introduction Consider the following discussion by Condoravdi and van der Torre [6]. “Example (Linguistic interpretation of Chisholm’s paradox) The most no- torious story from the deontic logic literature is known as Chisholm’s paradox: 1. a certain man ought to go to the assistance of his neighbours, 2. if he goes, he ought to tell them he is coming, 3. if he does not go, he ought not to tell them he is coming, 4. he does not go. Analyses of the three conditional obligations have led to preference-based de- ontic logic, temporal deontic logic, action deontic logic, non-monotonic deon- tic logic, and more. A more general linguistic analysis would also question the fourth sentence: what does it mean that the man does not go? Does it mean that he cannot go, that he intends not to go, or that he did not go? Taking into account the temporal perspective of the fourth premise and, more generally, the context in which the reasoning takes place constitutes new challenges for the logical analysis of the paradox.” [6] The example of Condoravdi and van der Torre suggests that a linguistic analysis of de- ontic paradoxes can be used to further develop the logic of obligations and permissions. In this paper, we take up their challenge, and we start the development of a semantics for such a linguistic interpretation. We use the following fragment of the miners sce- nario 1 to motivate, develop and validate our approach. As in the analysis of Chisholm’s 1 Kolodny and MacFarlane [12] and Willer [16] call it a paradox, while Cariani et al. [3] call it a puzzle. In this paper, we do not consider the question whether it is a paradox, and call it “the miners scenario.”