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This paper develops the framework of telling and knowledge operators earlier proposed for distinctions of mood and sentence types in the lexical verb (Davies 2006) to apply to non-inferential epistemic modal verbs. It consists of two parts: the first offers some background to the approach and sets out the formal model used; the second applies this model to two modal verbs. It considers the meanings of the modal verbs may (not) and might (not) as used in four different English sentence-types, with a view to assessing the different degrees of ‘loading’ towards a positive belief that they convey. Different kinds of meanings are suggested, one to do with degrees of a speaker’s commitment to what s/he is saying (‘presentational meaning’), and another to do with attitudes projected, by the speaker through the constructions s/he uses, onto the addressee(s) in a developing text (‘textual meaning’). In the case of the two modal verbs studied here, the textual meaning is said to be contrastive in relation to the speaker’s own ‘presentational meaning’.