UNDERSPECIFICATION AND LINGUISTIC INFORMATION


In this talk I'll argue that the underspecification phenomenon has
important consequences for the general architecture of grammar and for the
way we should represent linguistic information. As many people have noted,
there are at least two ways in which we can represent such information: a)
by means of structures (trees, strings, attribute-value graphs, etc.), or
b) by means of theories (sets of closed formulas) talking about such
structures. The latter perspective is exemplified by Mark Johnson's
first-order formalisation of Lexical-Functional Grammar (LFG),
formalisations of features using modal logic (Kracht, Blackburn) and
Blackburn & Gardent's rendering of LFG with the help of modal logic. If we
choose perspective a), it becomes difficult to represent underspecified
linguistic information, since such information by definition will admit
more than one structure. However, if we choose perspective b), and view
linguistic information in terms of theories, underspecification is no
longer a difficulty but something entirely expected: it is an exception
rather than the rule if a theory has precisely one minimal model. Theories
which have no models (overspecification) or more than one
(underspecification) are much more common.

In the talk I'll model the linguistic information that is connected with a
lexical entry as a theory talking about structures in various linguistic
dimensions (word order, dominance, f-structure, semantics,...). I call such
theories 'signs'. Signs, except for their part pertaining to semantics,
will be couched in a very poor fragment of predicate logic (universal
sentences with--essentially--no function symbols except individual
constants). Their semantics part will consist of a system of equations in a
richer fragment of classical logic. Signs for complex linguistic structures
can be obtained by "clicking together" atomic signs with the help of the
commutative Lambek Calculus, a variant of the logic underlying Categorial
Grammar. The basic requirement on signs is that they be consistent, i.e.
have (minimal) models.

The system as it is sketched here has obvious connections with LFG and
Categorial Grammar, but also with Tree Adjoining Grammars. I'll argue that
it has some advantages over these theories and that it is computationally
attractive.