some image logo

HOME

SEARCH

CURRENT ISSUE

REGULAR ISSUES

   Volume 1 (2005)

   Volume 2 (2006)

   Volume 3 (2007)

   Volume 4 (2008)

      Issue 1

      Issue 2

      Issue 3

      Issue 4

   Volume 5 (2009)

   Volume 6 (2010)

   Volume 7 (2011)

   Volume 8 (2012)

   Volume 9 (2013)

   Volume 10 (2014)

   Volume 11 (2015)

   Volume 12 (2016)

SPECIAL ISSUES

SURVEY ARTICLES

AUTHORS

ABOUT

SERVICE

LOGIN

FAQ

SUPPORT

CONTACT

VOLUME 4, ISSUE 1, PAPER 9


Normalisation Control in Deep Inference via Atomic Flows

©Alessio Guglielmi, University of Bath
©Tom Gundersen, University of Bath

Abstract
We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations. This allows us to prove, for propositional logic, a new and very general normalisation theorem, which contains cut elimination as a special case. We operate in deep inference, which is more general than other syntactic paradigms, and where normalisation is more difficult to control. We argue that atomic flows are a significant technical advance for normalisation theory, because 1) the technique they support is largely independent of syntax; 2) indeed, it is largely independent of logical inference rules; 3) they constitute a powerful geometric formalism, which is more intuitive than syntax.

Publication date: March 31, 2008

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-4(1:9)2008

Hit Counts: 12621

Creative Commons