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Abstract:
Locality in various forms (Kimball, 1973;
Frazier,1978; Gibson, 1998) has been advanced as an important
determinant of reading time patterns in both ambiguous and
unambiguous sentences. Often the conceptual basis of
locality is described in terms of reactivation of linguistic
representations in short-term memory.
This talk presents an alternative basis for such
reading time patterns in terms of the amount of information
processed. In particular, a method is presented for
calculating the amount of information received by a hearer from a
speaker producing a sentence generated by a grammar known to both
parties. This value is a natural explanation for reading
time from the cognitivist perspective on reading as an
information-processing task.
The method identifies each intermediate state of a
left-to-right parser with the set of partial derivations that
generate the prefix observed at that state. These partial
derivations look like trees with ``unexpanded'' nonterminal
symbols at some of their leaves. In the case of a top-down
parser with a non-left-recursive grammar, the set of such partial
parse trees is finite since the set of leftmost derivations is
finite. This entails no loss of generality since various
methods are available for removing left recursion. Then,
applying foundational work of Grenander (1967), one computes the
conditional entropy of the start symbol given the prefix, taking
the set of partial derivations as the set of possible
derivations. Unexpanded nonterminals are assigned their
expected entropy. Any tree structure that is completely
certain contributes zero entropy. In this way the
conditional entropy at each word is obtained. Subtracting
these gives the information conveyed. If semantic rules
mirror syntactic rules in a one-to-one fashion (as proposed,
e.g., by Steedman, 2000), then the information-processing work
performed by a completely efficient sentence comprehender is
given by this method.
This method differs from other ways of measuring
information content (e.g., Shannnon, 1951) in that the model of
grammar assumed is one that has context-free derivations, rather
than just n-grams.
Using explicit grammars for English stimuli, the
method is evaluated against experimentally observed reading times
on a variety of linguistic constructions, including the data
collected by Grodner et al. (2000) on subject and object relative
clauses.
References
Frazier, Lyn. (1978). On Comprehending
Sentences: Syntactic Parsing Strategies. Ph.D.
dissertation, University of Massachusetts, Amherst, MA.
Gibson, Edward. (1998). Linguistic
complexity: Locality of syntactic dependencies. Cognition,
68:1-76.
Grenander, Ulf (1967). Syntax-Controlled
Probabilities. Technical report, Brown University
Division of Applied Mathematics.
Grodner, Daniel, Watson, Duane, & Gibson,
Edward (2000). Locality effects on sentence
processing. Talk presented at CUNY 2000.
Kimball, John (1973). Seven principles of
surface structure parsing in natural language. Cognition,
2:15-47.
Shannon, Claude (1951). Prediction and
entropy of printed English. Bell System Technical Journal,
30:50-64.
Steedman, Mark (2000). The Syntactic
Process. MIT Press.
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