A suggestion is made for representing iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency. The formalization is such that normative sentences are represented as agentive sentences and therefore have history dependent truth conditions.
In contrast to investigations in alethic modal logic, in the construction of systems of deontic logic little attention has been paid to the iteration... of the deontic modalities.
L. Goble (1966, p. 197)
N. Belnap and P. Bartha (1995) present a formalization of iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency, due to Belnap, Perloff, and Xu (1996). In the present paper a simplification of Belnap and Bartha's approach is suggested. In order to support easy comparison with (1995), I shall take up Belnap and Bartha's discussion of R. Barcan Marcus' (1966) example
Parking on highways ought to be forbidden.
The simplified account underlines the power of stit theory and represents obligations, prohibitions and permissions as agentive sentences, as required by iteration. Therefore, in particular, the truth of obligations, prohibitions and permissions is it history dependent.