Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
1 Setting the stage: logics, prolog, theories
1.1 Summary
(1) We will use the programming language prolog to describe our language processing methods.
Prolog is a logic.
(2) We propose, following Montague and many others:
Each human language is a logic.
(3) We also propose:
a. Standard sentence recognizers can be naturally represented as logics.
(A “recognizer” is something that tells whether an input is a sentence or not.
Abstracting away from the “control” aspect of the problem, we see a recognizer as taking the input
as an axiom, and deducing the category of the input (if any).
We can implement the deduction relation in this logic in the logic of prolog. Then prolog acts as a
“metalanguage” for calculating proofs in the “object language” of the grammar.)
b. Standard sentence parsers can be naturally represented as logics.
(A “parser” is something that outputs a structural representation for each input that is a sentence,
and otherwise it tells us the input is not a sentence.
As a logic, we see a parser as taking the input as an axiom from which it deduces the structure of
the input (if any).)
All of the standard language processing methods can be properly understood from this very simple
perspective. 1
(4) What is a logic? A logic has three parts:
i. a language (a set of expressions) that has
ii. a “derives” relation ⊢ defined for it (a syntactic relation on expressions), and
iii. a semantics: expressions of the language have meanings.
a. The meaning of an expression is usually specified with a “model” that contains a semantic
valuation fuction that is often written with double brackets. So instead of writing
semantic_value(socrates_is_mortal)=true
we write
[[socrates_is_mortal]] = 1
b. Once the meanings are given, we can usually define an “entails” relation ⊨, sothatforanyset
of expressions Γ and any expression A, Γ ⊨ A means that every model that makes all sentences
in Γ true also makes A true.
And we expect the derives relation ⊢ should correspond to the ⊨ relation in some way: for
example, the logic might be sound and complete in the sense that, given any set of axioms Γ we
might be able to derive all and only the expressions that are entailed by Γ .
So a logic has three parts: it’s (i) a language, with (ii) a derives relation ⊢, and with (iii) meanings.
1 Cf. Shieber, Schabes, and Pereira (1993), Sikkel and Nijholt (1997). Recent work develops this perspective in the light of resource logical
treatments of language (Moortgat, 1996, for example), and seems to be leading towards a deeper and more principled understanding
of parsing and other linguistic processes. More on these ideas later.
4