NORMATIVE CHARACTERISTICS OF ACTIONS IN DYNAMIC DEONTIC LOGIC

In a series of recent papers, Kislov introduced a number of new normative characteristics of actions - permissible in the strict sense (in what follows I write 'strictly' instead of 'in the strict sense'), strictly forbidden, strictly obligatory, strictly indifferent, recommending-indifferent, and warning-indifferent. He defined them, in particular, in the context of a deontic version of propositional dynamic logic with a symbol for 'sanction' as the only propositional constant (in what follows, this logic will be referred to as PDL). He also suggested a map of deontic universe representing extensions of the standard and the new normative characteristics of actions. I find his characteristics of actions interesting because they reflect some intuitive normative ideas that are not reflected by standard characteristics. In this paper I examine the semantics of PDL and Kislov's map of deontic universe, and show that both should be corrected in some respects. First, I show that, in order for a PDL model to be deontically relevant, the following restriction on models should be imposed: in each PDL model <W, V>, V(nu) is a nonempty proper subclass of W. Second, I examine Kislov's map of deontic universe and point out three erroneous tenets behind it: 1) There are strictly indifferent actions. 2) Each strictly obligatory action is also strictly permissible (equivalently: each strictly forbidden action is such that not-performing it is strictly permissible). 3) Each (standardly) indifferent action is either warning-indifferent or recommending-indifferent. I conclude that the map of deontic universe should be corrected taking into account the following facts: 1) In models meeting the above restriction, there is no strictly indifferent action. 2) An action can be strictly obligatory without being strictly permissible, and equivalently an action can be strictly forbidden whereas not-performing it is not strictly permissible. 3) An action can be (standardly) indifferent without being warning-indifferent or recommending-indifferent. I also adduce some new examples of using Kislov's characteristics of actions for formalizing intuitive normative ideas.