Randomness, Structure and Causality - Agenda: Difference between revisions
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The Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts<br> | The Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts<br> | ||
Debowski, Lukasz (ldebowsk@ipipan.waw.pl<br> | Debowski, Lukasz (ldebowsk@ipipan.waw.pl)<br> | ||
Polish Academy of Sciences<br> | Polish Academy of Sciences<br> | ||
<br> | <br> | ||
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way. Besides the theorem, we will exhibit a few stochastic processes | way. Besides the theorem, we will exhibit a few stochastic processes | ||
to which this and similar statements can be related. | to which this and similar statements can be related. | ||
<br> | |||
<p> | <p> | ||
[[http://arxiv.org/abs/0810.3125]] and [[http://arxiv.org/abs/0911.5318]] | [[http://arxiv.org/abs/0810.3125]] and [[http://arxiv.org/abs/0911.5318]] |
Revision as of 18:40, 16 December 2010
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Abstracts
The Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts
Debowski, Lukasz (ldebowsk@ipipan.waw.pl)
Polish Academy of Sciences
We will present a new explanation for the distribution of words in
natural language which is grounded in information theory and inspired
by recent research in excess entropy. Namely, we will demonstrate a
theorem with the following informal statement: If a text of length $n$
describes $n^\beta$ independent facts in a repetitive way then the
text contains at least $n^\beta/\log n$ different words. In the
formal statement, two modeling postulates are adopted. Firstly, the
words are understood as nonterminal symbols of the shortest
grammar-based encoding of the text. Secondly, the text is assumed to
be emitted by a finite-energy strongly nonergodic source whereas the
facts are binary IID variables predictable in a shift-invariant
way. Besides the theorem, we will exhibit a few stochastic processes
to which this and similar statements can be related.