In general, it is best to understand a "System" as having two sub-components: an alethic one, for formulae with the 'assertive' mood operator device, and a 'boulomaic' one, for things like 'imperatives' and so on.
The Semantics for System G, then, comprise:
an alethic --truth-conditional-- component. For multiple values 0 to 1. Grice uses just 0 and 1, but in his work on 'intending', it is clear that he is into subjective probabilities of belief for which the continuum 0-1 is preferred (an intention thus involves a belief that the outcome has probability greater than 0.5 to be realised.
a boulomaic component. This includes the 'compliance' conditions.
And so on.
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