Normalisation Control in Deep Inference via Atomic Flows

Details Normalisation Control in Deep Inference via Atomic Flows Normalisation Control in Deep Inference via Atomic Flows

2007-09-08

arxiv.org/abs/0709.1205v3

LMCS 4 (1:9) 2008

Mathematics

Logic

Scientific paper

10.2168/LMCS-4(1:9)2008

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.

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