Improving the Tractable Lexicon Size for the Rational Speech Act Model
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2021-06-21
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en
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The Rational Speech Act model adapted to resolving misunderstandings in conversation
is conjectured to be intractable. A combinatorial explosion in searching through
the space of possible lexicons is likely responsible for this intractability. Coming from a
xed-parameter tractability view, where intractable problems can become tractable for
restricted input parameters, I have introduced and tested two constraints on possible
lexicons in an attempt to improve upon the feasibly computable lexicon size. Stemming
from an intuition that humans use these constraints as well, one constraint is the use
of knowledge or facts for generating lexicons. Some words can have very speci c and
unambiguous meanings. The other constraint is about the use of similarity or neighborliness
to generate new lexicons. The other person will likely have a similar meaning
for the same word. I named these constraints factual lexicons and neighboring lexicons.
The former is formalized as xing a certain amount of mappings of signal and referent
that are always existent. The latter is formalized as considering similar lexicons as compared
to the current one available to the agent. Both constraints were formalized in
the Human Language Constrained Rational Speech Act model. The results
indicate that factual lexicons improve to a lesser extent the time and space performance
of the model and result in degraded model accuracy when resolving misunderstandings.
Neighboring lexicons improve to a much larger extent time and space performance and
also improve upon accuracy. As of writing, both the intractability of the problem and
the xed-parameter tractability approach are unproven. Nevertheless, these results hint
at the capability of constraints to improve upon the feasibly computable lexicon size for
the RSA model. However, I am not convinced that the constraints are a xed-parameter
solution to an unproven problem.
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Faculteit der Sociale Wetenschappen