Thomas, Michael R.
(2004)
*A NON-CLASSICAL APPROACH TO MAXIMUM ENTROPY IN UNCERTAIN REASONING.*
Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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## Abstract

This thesis is concerned with the question “Given a set of knowledge about propositional variables, what is the ‘best’ way to assign probability values to those variables?” I present here an approach to this question based upon a philosophical concept of negation and its role in perception. This concept is discussed in detail before a mathematical analysis of it is presented, in the form of structures in propositional logic which, it is claimed, embody the principles of the underlying philosophy. There follows the definition and mathematical characterisation of an inference process which utilises these logical structures and also adheres closely to the principles of Maximum Entropy. The properties of this inference process are analysed and discussed. Another inference process is then described based upon a modified version of the philosophical principles defined earlier. A class of graphs is found which are intimately connected with this inference process, and two attempts at characterising this class are presented. 6

Item Type: | Thesis (Doctoral) |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 21 Jul 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/409 |

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