Categorial grammar and lexical-functional grammar

This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.
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Reinhard Muskens (2010). New Directions in Type-Theoretic Grammars. Journal of Logic, Language and Information 19 (2):129-136.

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