Linear Logic for Natural Language - An Informal Meeting

Recent work has shown how a fragment of linear logic can be used as a meta-language for building up formal semantic analyses of natural language sentences. Other work has shown how ideas from linear logic are useful in categorial approaches to the syntax of natural language.

We decided to have a meeting dedicated to the theme ``Linear logic for Natural Language" at the School of Computer Science, University of Birmingham. Talks are on Thursday 20th March, from 9:30 am till 4 o'clock pm in the Law Faculty, Faculty Board Room.

Speakers are (provisionally) Dr Dick Crouch, Dr Josef van Genabith, Dr Mark Hepple and Dr Valeria de Paiva. There is a list of abstracts below.

A map of the University of Birmingham campus can be found here.

Abstracts:

A Tutorial on Linear Logic for Natural Language - Dick Crouch
This talk will introduce some of the ideas behind the use of linear logic in natural language analysis. It will be slanted more towards the use of LL for semantic analysis, but will also touch on its use in syntax.

  1. An ignoramus's overview of linear logic

    This will highlight some properties of linear logic that are particularly salient to its use in natural language analysis.

  2. Linear logic as a glue language:

    This will describe how a fragment of LL can be used as a meta-language for glueing together the meanings of words in a sentence to obtain the meaning of the sentence.

  3. This describes some extensions to the glue language approach to handle the influence of context on sentence meanings

  4. Linear logic and syntax

    Non-commutative LL and categorial grammars

  5. Open issues
Linear Logic and Categorial Grammar - Mark Hepple
Grammars are formal systems that are used within linguistics to give an account of the principles governing how the words of a language may be combined to form sentences. Categorial grammars are a class of grammar formalisms that bear a clear relation to logics, most obviously implicational logics. This talk will discuss the relevance of linear logic and related resource logics to work in categorial grammar. Topics to be addressed include the basics of categorial linguistic analysis, the relation of structure sensitivity in resource logics to notions of linguistic structure, mixed categorial logics, and the use of labelled deduction variants of linear logic as a general framework for formulating categorial grammars.

Ellipsis and Linear Logic Derivations - Dick Crouch
Mary Dalrymple and others have shown how compositions of meanings can be represented as logical derivations in a fragment of linear logic. This talks extends her analysis to show how (a) the resource conscious nature of linear logic can be used to model context update in natural language interpretation, and (b) how sets of constraints on possible derivations can be used to represent semantic underspecification. Having done this, one can give an elegant analysis of ellipsis in natural language, whereby ellipses can be resolved by making substitutions on the constraints determining how the meaning of the antecedent expression is derived. This approach is compared to a currently influential treatment of ellipsis in terms of higher order unification.

Glue Language Semantics and Dynamics: A Hybrid Approach - Josef van Genabith
This talk presents a merger of developments in dynamic semantics [DRT, DMG] with a linear logic based glue language approach to semantic composition [Dalrymple et. al.]. The merger combines deductive approaches to quantifier scope with dynamic semantics. A fine grained approach to underspecification can be provided in terms of constraints on derivations. Sets of linear logic glue language premises (plus constraints) can be given a QLF or a UDRS style semantics. The approach is "hybrid" in the sense that the dynamics (context update and interpretation in context) of the resulting system is located in the meaning representation language slots rather than in the linear logic glue language derivations.

xSLAM: a machine for computing linear lambda terms - Valeria de Paiva
I will introduce some of the basic ideas of the x-SLAM (explicit substitutions linear abstract machines) project. This project (joint work with Dr Eike Ritter) has just started and we can show some of the difficulties and some of the ways of getting around these, when computing with linear lambda terms. The goal is to discuss whether this functional programming tool can be useful when doing linguistic analyses.


Dr V.C.V. de Paiva
University of Birmingham, School of Computer Science,
Edgbbaston
Birmingham B15 2TT. United Kingdom.
Phone: (+44) 121 414 4766
Fax: (+44) 121 414 4281
Email: vdp@cs.bham.ac.uk