# Reasoning by term rewriting

Bulmer, Michael (1995) Reasoning by term rewriting. PhD thesis, University of Tasmania.

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## Abstract

We propose a broad system for reasoning by term rewriting. Our general
aim is to capture mathematical and scientific reasoning in a coherent system.
To this end we introduce several new processes which allow concrete
descriptions of standard notions.
For deductive reasoning we extend traditional methods for finding canonical
rewrite systems to a general method for systems involving both equations
and inequations. We introduce the notion of side conditions for nontheorems
and show how they provide a new kind of meta-reasoning whereby
an automated reasoner can determine why it failed to prove a given statement.
A method for the automatic proof of inductive theorems by an analogue
of mathematical induction is also presented.
A new algorithm is given for inductively generating conjectures (function
equations) from a set of observations (a rewrite database). This is a process
of scientific induction and we prove some fundamental results linking it to
mathematical induction. Comparisons are given with standard inductive
learning systems, such as FOIL, to illustrate the expressive power of our
algorithm.
We obtain probabilistic measures of the strength of a single conjecture using
statistical testing and an information measure. For a collection of conjectures
we are then able to quantify Popper's well-known falsifiability criterion
for the strength of a theory. We also introduce a non-standard modal operator
to extended our deductive reasoning to reasoning with conjectures.
We use belief dynamics as the framework of an implementation of the reasoning
methods. Consistency analysis, using the same canonical-form algorithm
introduced earlier, allows the reasoner to build a belief set from given
knowledge and to form a working theory from the conjectures it makes.
Again a meta-reasoning is introduced, with the reasoner then able to decide
what experiments need to be carried out when it conjectures more than one
consistent theory from given set of observations.
Dialogues with the reasoner, generated by a prototype implementation of
the work in the thesis, are given to illustrate its behaviour and the links
between the internal language it uses and natural language.

Item Type: Thesis - PhD Bulmer, Michael Rewriting systems (Computer science), Induction (Mathematics), Prediction (Logic), Logic, Symbolic and mathematical The Author Copyright 1997 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s). Includes bibliographical references (leaves 127-128). Thesis (Ph.D.)--University of Tasmania, 1997 25 Nov 2014 00:46 11 Mar 2016 05:55 View statistics for this item