A Dyadic Operator for the Gradation of Desirability

We propose a normal modal deontic logic based on a dyadic operator, similar in structure to the temporal “until”. By bringing significant expressiveness to the logic, it allows both the definition of a monadic desirability operator similar to the SDL obligation, and the expression of the relative level of desirability of target formulae. The interpretation of this logic on a linear structure of worlds ordered by desirability makes its semantics more intuitive and concrete than the SDL deontic accessibility relation. We also show that the core modality of the logic permits to represent the Chisholm and Forrester paradoxes of deontic logic in a more precise way, which does not lead to inconsistencies.