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 {{Randomness, Structure and Causality}}   {{Randomness, Structure and Causality}} 
   
−   +  [[Media:Agenda.pdfAgenda PDF]] 
−  == Abstracts ==
 
−   
−  <br>
 
−   
−  The Vocabulary of GrammarBased 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 <math>n</math>
 
−  describes <math>n^\beta</math> independent facts in a repetitive way then the
 
−  text contains at least <math>n^\beta/\log n</math> different words. In the
 
−  formal statement, two modeling postulates are adopted. Firstly, the
 
−  words are understood as nonterminal symbols of the shortest
 
−  grammarbased encoding of the text. Secondly, the text is assumed to
 
−  be emitted by a finiteenergy strongly nonergodic source whereas the
 
−  facts are binary IID variables predictable in a shiftinvariant
 
−  way. Besides the theorem, we will exhibit a few stochastic processes
 
−  to which this and similar statements can be related.
 
−  <br>
 
−  <br>
 
−   
−  Links: [[http://arxiv.org/abs/0810.3125]] and [[http://arxiv.org/abs/0911.5318]]
 