Type Theoretical Intensional Logic
Already in 1951, Alonzo Church had developed an intensional calculus. The semantical motivations were explained expressively, of course without those tools that we know in establishing semantics for modal logic in a formal way, because they had not been invented yet that time: Church has not provided formal semantic definitions.
Later, possible world approach to semantics provided tools for a comprehensive study in intensional semantics. Richard Montague could preserve the most important advantages of Church's intensional calculus in his system. Unlike its forerunner, Montague grammar was built in a purely semantical way: a simpler treatment became possible, thank to the new formal tools invented since Church's work.
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