Linear Logic for Meaning Assembly

Dalrymple, Lamping, Pereira, Saraswat 1995

Dalrymple et al describe a system for mapping LFG structures into semantic representations. The semantic representation produced is basically a typed lambda calculus expression, where the type specifies how the parameters relate to the LFG structure. (The "type" is actually a "linear logic expression".) The reason that they use linear logic is that it enforces the constraint that every piece of meaning should be used exactly once.

To find the meaning of an LFG expression, first calculate the set of semantic representations for the expression and any of its children. For example, if we want to know the semantic representation of the sentence "Bill saw Mary," then we construct the following set of semantic representations:

• [[Bill]] = Bill: g

• [[Mary]] = Mary: h

• [[saw]] = :

(f.subj (f.obj f)

The pieces can then be freely combined, but they must match up with the LFG structure.

This system can handle both modifiers and scoping. Modifiers look like:

• [[obviously]] = : f f

For scoping, we use more complex NP denotations. For example, everyone would look something like:

• [[everyone]] = : (h scope) scope

This gives the right scope restrictions, and allows us to preserve scope ambiguity in our semantic representation.

Bibtex

```@InProceedings{dalrymple1995,
author =       {Mary Dalrymple, John Lamping, Fernando Pereira,
and Vijay Saraswat},
title =        {Linear Logic for Meaning Assembly},
booktitle =    {Proceedings of CLNLP},
url = "citeseer.nj.nec.com/dalrymple95linear.html",
year =      1995,
}```