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Coling 2000 Tutorial Announcement


Philippe de Groote: Introduction to Categorial Type Logic

The goal of this tutorial, which is designed for beginers, is to give a first account of the type-logical systems underlying modern categorial grammars.

As a paradigmatic example of such type-logical systems, we will mainly focus on the Lambek calculus. On a theoretical side, we will first introduce the Lambek calculus as a logical system and present its model theory and its proof theory. On an applicative side, we will motivate the laws of the Lambek calculus by means of several linguistic examples. In particular, wh-extraction and non-constituent coordination will illustrate the power of hypothetical reasoning.

One of the advantages of the categorial grammars is that they offer a transparent interface between syntax and semantics. This topic will be demonstrated by presenting Montague-like semantics in the categorial setting.

Finally, we will discuss different limitations of the Lambek calculus by giving several examples of overgeneration. These examples motivate the need for type-logical systems extending the Lambek calculus. As examples of such extensions, we will present multimodal systems.


Outline of the tutorial:

            • The origin of Categorial Grammars.
            • The Lambek Calculus, its syntax and semantics.
            • Categorial Grammars and Montague's Semantics.
            • Limitations of the Lambek Calculus. Multimodal Systems.

             


Reading:

B. Carpenter. "Type-Logical Semantics". MIT Press (1997).

M. Moortgat. "Categorial type logics". In J. van Benthem and A. ter Meulen (Eds.),
Handbook of Logic and Language, Elsevier (1997)

G.V. Morrill. "Type Logical Grammar: Categorial Logic of Signs". Kluwer Academic Publishers, Dordrecht (1994).

 

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