|
|
(31 intermediate revisions by 2 users not shown) |
Line 1: |
Line 1: |
| {{Randomness, Structure and Causality}} | | {{Randomness, Structure and Causality}} |
|
| |
|
| | | [[Media:Agenda.pdf|Agenda PDF]] |
| == Abstracts ==
| |
| | |
| <br>
| |
| | |
| The Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts<br>
| |
| | |
| Debowski, Lukasz (ldebowsk@ipipan.waw.pl<br>
| |
| Polish Academy of Sciences<br>
| |
| <br>
| |
| <p>
| |
| 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.
| |
| | |
| <p>
| |
| | |
| [[http://arxiv.org/abs/0810.3125]] and [[http://arxiv.org/abs/0911.5318]] | |