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:

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.

   • resource sensitiviy of LL and using word meanings exactly once
   • semantic derivations as LL proofs
   • setting up the premises
   • semantic ambiguity and multiple derivations

3. This describes some extensions to the glue language approach to handle the influence of context on sentence meanings
   • contextual update and underspecification
   • LL and update
   • constraints on glue language derivations

4. Linear logic and syntax

   Non-commutative LL and categorial grammars

5. Open issues
   • coverage
   • fragments and ill-formed input
   • reversibility
   • updates and dynamics
   • implementation
   • combining glue languages and linear syntax

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.