On the Refinement of the Model for Deontic Dynamic Logic with the Reductionist Semantics (Reply to E.V. Borisov)

The article is a response to some E.V. Borisov’s criticism regarding the normative characteristics of actions expressed in the reductionist version of deontic propositional dynamic logic with the propositional constant “sanction”. First, the agreement is expressed with the requirement, when defining models for this logic, to state that the binary relations that determine the interpretation of actions must be serial. Second, the need to indicate that the interpretation of the propositional constant “sanction” must be a nonempty proper subclass of the set of possible worlds of the model is accepted. Third, it is agreed to correct the areas of the normative characteristics of actions in the map of deontic universe since Borisov substantiated the absence of strictly indifferent actions in models under consideration. Critical remarks about the necessity of a direct indication of both the seriality of the binary relation that determines the interpretation of actions and the fact that the interpretation area of the propositional constant “sanction” is nonempty and nonuniversal are important. They must be taken into account in further work on the construction and study of the properties of the corresponding deontic logics with the reductionist semantics and other logics of this type. The agreement with the most conceptual remark about the emptiness of the area of strictly indifferent actions is accompanied by an explanation that the concept of “actions normatively indifferent in the strict sense” is interesting from the point of view of interpretation since it distinguishes a class of actions that, both when performing them and when refraining from their fulfillment inevitably, leads to a state of affairs that is not assessed negatively, that is, not to a “sanction”. The reductionist approach to the semantic plans of deontic logic based on propositional dynamic logic, the refinement of which led to critical remarks, does not (among other things) solve the problem of preserving the semantic status of strictly indifferent actions. The causes of the errors and the ways of searching for semantic formulations that are more consistent with deontic contexts are analyzed. Among the latter is the search for an adequate semantic formulation of the concept of “refraining from action”, as well as a radical rejection of the reductionist semantics with the propositional constant “sanction”.

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