Language and Logic introductory course:
Introduction to Abstract Categorial Grammars: Foundations and main properties.

• Philippe de Groote ()
• Sylvain Salvati ()

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The abstract categorial grammar (ACG) introduced by de Groote (2001) derives from the categorial and type-logical tradition, and is based on principles that may be traced back to both Curry and Lambek. This course will focus on the main concepts underlying the ACG. We will first motivate the formalism by showing how it derives from the categorial grammar tradition. We will then illustrate the expressive power of the ACG by showing how several grammatical formalisms may be encoded as ACGs. We will review the fundamental properties (membership, universal membership, emptyness...), and establish a formal relation between ACG and linear logic. Finally, we will review possible extensions of the formalism, and discuss their properties.