We obtain two results about the proof complexity of deep inference:(1) Deep-inference proof
systems are as powerful as Frege ones, even when both are extended with the Tseitin …

Linear inferences are sound implications of propositional logic where each variable appears
exactly once in the premiss and conclusion. We consider a specific set of these inferences …

We consider the fragment of deep inference free of compression mechanisms and compare
its proof complexity to other systems, utilising 'atomic flows' to examine size of proofs …

We consider deep inference proof formalisms, which are flexible enough to embed many
widely used proof systems, and construe compression mechanisms 'cut'and 'dag'in a way …

We consider the proof complexity of the minimal complete fragment of standard deep
inference, denoted KS. To examine the size of proofs we employ atomic flows, diagrams that …

Ten Years of Deep Inference Page 1 Ten Years of Deep Inference Alessio Guglielmi University
of Bath and LORIA & INRIA Nancy-Grand Est Joint work with Paola Bruscoli, Tom Gundersen …

Normalisation with Atomic Flows Page 1 Normalisation with Atomic Flows Alessio Guglielmi
University of Bath and LORIA & INRIA Nancy-Grand Est Joint work with Paola Bruscoli, Tom …

Some News on the Proof Complexity of Deep Inference Page 1 Some News on the Proof
Complexity of Deep Inference Alessio Guglielmi University of Bath and LORIA & INRIA …