A Note on Nesting in Dyadic Deontic Logic
This work addresses a theoretical gap in a foundational logic for reasoning with dyadic obligations, but it is incremental as it builds on known properties of system G.
The paper tackles the problem of nested modal operators in Aqvist's dyadic deontic logic system G, showing that any formula with nesting is equivalent to a formula without nesting and that the universal modality is definable in terms of the deontic modality.
The paper reports on some results concerning Aqvist's dyadic logic known as system G, which is one of the most influential logics for reasoning with dyadic obligations ("it ought to be the case that ... if it is the case that ..."). Although this logic has been known in the literature for a while, many of its properties still await in-depth consideration. In this short paper we show: that any formula in system G including nested modal operators is equivalent to some formula with no nesting; that the universal modality introduced by Aqvist in the first presentation of the system is definable in terms of the deontic modality.