Languages with self-reference. II: Knowledge, belief, and modality (Q1101099)

[For part I see ibid. 25, 301-322 (1985; Zbl 0581.03005).] Negative results of Montague and Thomason have diverted research in propositional attitudes away from syntactic (``first-order'') approaches, encouraging modal formalisms instead, especially in representing epistemic notions. We show that modal logics are on no firmer ground than first-order ones when equally endowed with substitutive self-reference. Nonetheless, there may still be remedies, hinging in part upon a distinction between ``dynamic'' and ``static'' notions of provability and belief (an earlier version of this paper emphasized a somewhat different distinction).