Self-Reference, Knowledge, Belief, and Modality

Donald Perlis

An apparently negative result of Montague has diverted research in formal modalities away from syntactic ("first-order") approaches, encouraging rather weak and semantically complex modal formalisms, especially in representing epistemic notions. We show that, Montague notwithstanding, consistent and straightforward first-order syntactic treatments of modality are possible, especially for belief and knowledge; that the usual modal treatments are on no firmer ground than first-order ones when endowed with self-reference; and that in the latter case there still are remedies.

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