Model-Theoretic System G

Jones, in commentary to "Grice's Section VIII":

"I think it's correct to describe this as a "truth conditional" semantics (though more often it would be called "model theoretic", which usually is but I think need not necessarily be truth conditional)."

Good point. So, one wonders.

Since System G -- as opposed to Grice's System Q -- should have ! as a denominational type, System G (or more properly System G_HP -- cfr. Jones's System C_R after Carnap) the question is made about the semantics for these formulae.

Such as, in interpreted contexts:

"Close the door!"

and stuff.