Thursday, April 4, 2013

Pattern Theory, PTML, and Probabilistic XML


In Prolegomena to an XML schema for pattern theory, a genesis for PTML (Pattern-Theoretic Markup Language) is specified. A key aspect of pattern theory is being able to define probabilities over structures in the theory (configurations). The following developments in XML could be a useful connection to the probability model of PTML:

Probabilistic XML: A Data Model for the Web
Pierre Senellart
Université Pierre et Marie Curie, Paris, France, June 2012
pierre.senellart.com/publications/senellart2012probabilistic.pdf

Here, a probabilistic XML space, abbreviated px-space, is defined as a probability space over XML documents. Random sample documents are generated from a p-document, a tree model similar to an XML document that includes a probabilistic process for generating a random document. (See above reference for details.)




Pattern Theory references:

Lectures in Pattern Theory: Volume 1: Pattern Synthesis
Author: Ulf Grenander
Publisher: Springer, 1976
ISBN: 0387901744, 9780387901749
Length: 509 pages

Lectures in Pattern Theory: Volume 2: Pattern Analysis
Author: Ulf Grenander
Publisher: Springer, 1978
ISBN: 0387903100, 9780387903101
Length: 616 pages

Lectures in Pattern Theory: Volume 3: Regular Structures
Author: Ulf Grenander
Publisher: Springer, 1981
ISBN: 038790560X, 9780387905600
Length: 569 pages