Arnould Bayart's Modal Completeness Theorems (translated with an introduction and commentary)

Max J. Cresswell


In 1958 Arnould Bayart, 1911-1998, produced a semantics for first and second-order S5 modal logic, and in 1959 a completeness proof for first- order S5, and what he calls a ‘quasi-completeness’ proof for second-order S5. The 1959 paper, is the first completeness proof for modal predicate logic based on the Henkin construction of maximal consistent sets, and indeed may be the earliest application of the Henkin method even to propositional modal logic. The semantics is in terms of possible worlds,which, Bayart notes, can be anything at all. The present paper provides an English translation of both these papers together with an historical introduction and a logical commentary.


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