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250views
15 years 5 months ago
Algorithmic Information Theory
"The aim of this book is to present the strongest possible version of G¨odel's incompleteness theorem, using an information-theoretic approach based on the size of com...
G J Chaitin
SYNTHESE
2008
88views more  SYNTHESE 2008»
13 years 7 months ago
Interpolation in computing science: the semantics of modularization
The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended to many other logical frameworks and is being applied in s...
Gerard R. Renardel de Lavalette
IGPL
2008
124views more  IGPL 2008»
13 years 6 months ago
The Ricean Objection: An Analogue of Rice's Theorem for First-order Theories
We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order t...
Igor Carboni Oliveira, Walter Alexandre Carnielli
TPHOL
2007
IEEE
14 years 1 months ago
Formalising Generalised Substitutions
Abstract. We use the theorem prover Isabelle to formalise and machinecheck results of the theory of generalised substitutions given by Dunne and used in the B method. We describe t...
Jeremy E. Dawson
DIS
2007
Springer
14 years 1 months ago
Computational Discovery in Pure Mathematics
Abstract. We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated th...
Simon Colton