Interpreting Computing, Mathematics and Logic within the
SP Framework
'Computing' as information compression by multiple alignment, unification and search
Journal of Universal Computer Science 5(11), 776-815, 1999 (from
2007-01-01, this journal will be an open-access journal and all papers,
including this one, may be downloaded without any charge),
PDF,
uk.arxiv.org/abs/cs.AI/0307013.
A short version of this article was presented at the British Colloquium for Theoretical Computer Science (BCTCS15),
Keele University, April 1999.
This paper argues that the operations of a "Universal Turing Machine" (UTM) and
equivalent mechanisms such as the "Post Canonical System" (PCS) - which are
widely accepted as definitions of the concept of 'computing' -
may be interpreted as information compression by multiple alignment,
unification and search (ICMAUS).
The motivation for this interpretation is that it suggests ways in which the
UTM or PCS model may be augmented to create a proposed new computing system
designed to exploit the ICMAUS principles as fully as possible. The provision
of a relatively sophisticated search mechanism in the proposed 'SP' system
appears to open the door to the integration and simplification
of a range of functions including unsupervised inductive learning, best-match
pattern recognition and information retrieval, probabilistic reasoning,
planning and problem solving, and others. Detailed consideration of how
the ICMAUS principles may be applied to these functions is outside the
scope of this article but relevant sources are cited in the article.
Mathematics and
logic as information compression by multiple alignment, unification and
search.
School of Informatics Report, March, 2002. PDF,
PDF.ZIP,
PS, PS.ZIP. Archive:
http://uk.arxiv.org/abs/cs.AI/0302015
This paper describes evidence in support of the conjecture that mathematics,
logic and related disciplines such as theoretical linguistics and computer
programming may be understood as information compression by multiple alignment,
unification and search. The case is made both in terms of the static forms
and structures of maths and logic etc and in terms of the dynamic processes
of mathematical calculation and logical inference. This paper supersedes the
two below.
Information compression and logic.
SEECS Report CS-JGW-95-3, December 1995. Postscript,
Compressed Postscript.
Logic as information compression by multiple alignment,
unification and search.
SEECS Report CS-JGW-95-4.1, October 1996.
Postscript,
Compressed Postscript.
These two papers (which are superseded by the one immediately above)
focus on how 'logic' may be understood
in terms of information compression by multiple alignment, unification
and search. The first paper is an extended introduction to the second.
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