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GRAMMATICAL RESOURCES: LOGIC, STRUCTURE, CONTROL

MOORTGAT and OEHRLE

 Logic & Language

Foundational
 

COURSE DESCRIPTION

The aim of this course, following the slogan `Cognition=Computation', is to model the cognitive abilities underlying knowledge and use of language as a `logic of grammar': a specialized deductive system, attuned to the task of reasoning about the composition of grammatical form and meaning. To carry out such a program, we have to address two central questions:
  • What are the constants of grammatical reasoning? Can we provide an explanation for the uniformity of the form/meaning correspondence across languages in terms of this vocabulary of logical constants, together with the deductive principles governing their use?
  • How can we reconcile the idea of grammatical constants/invariants with the differences between languages, that is, with structural variation in the realization of the form/meaning correspondence?
Our approach combines ideas from two research traditions: linear logic and categorial grammar. Our starting point is a base logic characterizing the core notion of grammatical composition. The base logic provides product connectives (for the assembly of grammatical material) and corresponding implications (modelling grammatical incompleteness). The product and implication constants satisfy basic principles of residuation, yielding rules of use and proof. These inference rules (introduction/elimination of the grammatical constants) provide the interface to a derivational theory of meaning via the Curry-Howard interpretation of proofs.

The base logic, in our set-up, identifies the logical core of the composition relation by carefully factoring out structural aspects of grammatical reasoning that could be language-specific. Cross-linguistic variation is obtained by combining the base logic with packages of structural postulates. Our treatment of structural resource management has two key features that make it possible to overcome the limitations of `classical' categorial approaches. First, we consider the grammar logic as essentially a multimodal system: different composition operations, each with their individual structural properties, live together and interact. Secondly, structural inferences are not globally available, but lexically anchored and under the explicit control of licensing features. These control features have the status of logical constants in their own right.

The course consists of two parts. During the first week, we develop the grammatical architecture described above. The second week, we shift to a format of computer lab sessions where students can gain hands-on experience with the framework using the grammar development environment GRAIL. We illustrate the fine-tuning of structural resource management on the basis of a number of contrastive studies including extraction, head adjunction (Romance cliticization, Germanic verb clusters), binding (quantification and anaphora).

LITERATURE

Follow this link for some extra web resources.

Michael Moortgat (1997) `Categorial Type Logics'. Extract from Chapter Two in Van Benthem and ter Meulen (eds.) Handbook of Logic and Language. Elsevier/MIT Press. (PDF Document)

Michael Moortgat (1999) `Constants of Grammatical Reasoning'. To appear in Bouma, Hinrichs, Krijff & Oehrle (eds.) Constraints and Resources in Natural Language Syntax and Semantics, CSLI, Stanford (Postscript Document)

Richard T. Oehrle (1999) `Multi-Modal Type-Logical Grammar'. To appear in Borsley and Borjars (eds.) Non-Transformational Syntax, Blackwell (Postscript Document)

Richard Moot (1998) `Grail: An Automated Proof Assistant for Categorial Grammar Logics'. Proceedings `Calculemus and Types 98: User Interfaces for Theorem Provers'. Eindhoven. (Postscript Document)

Richard Moot (1998) `User's Guide to Grail 2.0'. (Postscript Document)