Workshop on New Directions in Type-theoretic Grammars

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The Workshop on New Directions in Type-theoretic Grammars (NDTTG 2007) was organized as part of the European Summer School on Logic, Language and Information 2007, (ESSLLI 2007), which was be held in Dublin, 6 - 17 August, 2007. The workshop dates were August 6 - 10, 2007.

Workshop Organizer:
Reinhard Muskens

Workshop Purpose:
In 1961 Haskell Curry published his by now famous paper on 'Some Logical Aspects of Grammatical Structure'. In this paper (large parts of which had already been written in the 1940's) he made a distinction between the 'tectogrammatics' and 'phenogrammatics' of language (a distinction similar to that between abstract syntax and concrete syntax in compiler theory), while also arguing against directionality in the type system used for language description. In 1953 Bar-Hillel had introduced a distinction between categories seeking material to their right and categories seeking material to the left. To date most categorial grammarians follow Bar-Hillel in this, but in Curry's architecture phenogrammatical structure can take care of word order, making directionality unnecessary.

Curry's proposal was part of a classical phase in categorial grammar that started with Ajdukiewicz's paper on syntactic connexity and also included Joachim Lambek's pivotal work on the introduction of hypothetical reasoning. It led to many follow-ups. For example, in Richard Montague's work the tectogrammatics/phenogrammatics distinction reappeared as one between analysis trees and surface strings, while Montague also added a level of meaning as a third component. The grammatical architecture thus became one in which a central abstract component is interpreted on two levels. An explicit connection between Montague's set-up and that of Curry was given in David Dowty's work in the 1980's. Also in the 1980's, Aarne Ranta used the idea in a constructive type theory setting, while Reinhard Muskens used it for his Partial Montague Grammar and Johan van Benthem explored the logical and linguistic implications of LP*, the undirected version of the Lambek Calculus, or, in other words, the logic of simply typed linear lambda terms. Later years brought Richard Oehrle's insight that the interpreting levels of the theory (not only semantics but also phenogrammar) can be represented with the help of lambda terms. Since the central abstract component consists of LP* derivations in Oehrle's set-up, equivalent with linear lambda terms, in fact all levels of the grammar can now be represented with the help of lambda terms and the typed lambda calculus becomes the central mechanism for grammatical description (as it had been in Cresswell's lambda-categorial languages).

Since the turn of the century there has been a heightened activity within a series of type-theoretical formalisms bearing a family resemblance to one another. All of these adopt the pheno/tecto distinction or undirectedness in one way or another and claim various descriptive and formal advantages. We mention Abstract Categorial Grammars (de Groote), De Saussure Grammar (Kracht), Minimalist Categorial Grammars (Lecomte, Retore), Lambda Grammars (Muskens), Higher Order Grammar (Pollard), and the Grammatical Framework (Ranta). The workshop intends to bring together researchers in this now very active field. It aims to provide a forum for advanced PhD students and researchers, enabling them to present their work and to discuss it with colleagues who work in the broad subject areas represented at ESSLLI.

Invited Speakers:

Workshop Programme Committee:

Important Dates:

Acknowledgement:
We gratefully acknowledge support from the Netherlands Organisation for Scientific Research (NWO).