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Jeřábek showed that analytic propositional-logic deep-inference proofs can be constructed in quasipolynomial time from nonanalytic proofs. In this work, we improve on that as follows: 1) we significantly simplify the technique; 2) our normalisation procedure is direct, i.e., it is internal to deep inference. The paper is self-contained, and provides a… (More)

- Alessio Guglielmi, Tom Gundersen
- Logical Methods in Computer Science
- 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… (More)

- Alessio Guglielmi, Tom Gundersen, Michel Parigot
- RTA
- 2010

In usual proof systems, like the sequent calculus, only a very limited way of combining proofs is available through the tree structure. We present in this paper a logic-independent proof calculus, where proofs can be freely composed by connectives, and prove its basic properties. The main advantage of this proof calculus is that it allows to avoid certain… (More)

- Alessio Guglielmi, Tom Gundersen, Lutz Straßburger
- 2010 25th Annual IEEE Symposium on Logic in…
- 2010

This work belongs to a wider effort aimed at eliminating syntactic bureaucracy from proof systems. In this paper, we present a novel cut elimination procedure for classical propositional logic. It is based on the recently introduced `atomic flows': they are purely graphical devices that abstract away from much of the typical bureaucracy of proofs. We make… (More)

- Paola Bruscoli, Alessio Guglielmi, Tom Gundersen, Michel Parigot
- Logical Methods in Computer Science
- 2009

Jeřábek showed that analytic propositional-logic deep-inference proofs can be constructed in quasipolynomial time from nonanalytic proofs. In this work, we improve on that as follows: 1) we significantly simplify the technique; 2) our normalisation procedure is direct, i.e., it is internal to deep inference. The paper is self-contained, and provides a… (More)

- Tom Gundersen
- 2009

- Tom Gundersen, Willem Heijltjes, Michel Parigot
- 2013 28th Annual ACM/IEEE Symposium on Logic in…
- 2013

An explicit -- sharing lambda-calculus is presented, based on a Curry -- Howard-style interpretation of the deep inference proof formalism. Duplication of subterms during reduction proceeds 'atomically', i.e. on individual constructors, similar to optimal graph reduction in the style of Lamping. The calculus preserves strong normalisation with respect to… (More)

- Tom Gundersen, Willem Heijltjes, Michel Parigot
- LPAR
- 2013

Jeřábek showed in 2008 that cuts in propositional-logic deep-inference proofs can be eliminated in quasipolynomial time. The proof is an indirect one relying on a result of Atserias, Galesi and Pudlák about monotone sequent calculus and a correspondence between this system and cut-free deep-inference proofs. In this paper we give a direct proof of Jeřábek's… (More)

- T Gundersen, E Ramírez-García, J Randa
- Scandinavian audiology
- 1984

Extracochlear electrical stimulation was carried out in 7 patients. We used square-wave signals. Electrode positions at the oval and round window showed the lowest current thresholds. The threshold of sound sensations elicited by electrical stimulation was higher in the high frequency than in the low frequency range. All 7 patients had hearing sensations… (More)