In linguistics, formal semantics seeks to understand linguistic meaning by constructing precise mathematical models of the principles that speakers use to define relations between expressions in a natural language and the world that supports meaningful discourse. The mathematical tools used are the confluence of formal logic and formal language theory, especially typed lambda calculi.
Linguists rarely employed formal semantics until Richard Montague showed how English (or any natural language) could be treated like a formal language. His contribution to linguistic semantics, which is now known as Montague grammar, was the basis for further developments, like the categorial grammar of Bar-Hillel and colleagues, and the more recent type-logical semantics (or grammar) based on Lambek calculus.
Another line of inquiry, using linear logic, is Glue semantics, which is based on the idea of "interpretation as deduction", closely related to the "parsing as deduction" paradigm of categorial grammar.
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