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This article explores Herbrand’s theorem as the source of a natural notion of abstract proof object for classical logic, embodying the “essence” of a sequent calculus proof. We see how to view a calculus of abstract Herbrand proofs (Herbrand nets) as an analytic proof system with syntactic cut-elimination. Herbrand nets can also be seen as… (More)

We give a calculus of proof-nets for classical propositional logic. These nets improve on a proposal due to Robinson by validating the associativity and commutativity of contraction, and provide canonical representants for classical sequent proofs modulo natural equivalences. We present the relationship between sequent proofs and proof-nets as an annotated… (More)

We set out to find something that corresponds to deep inference in the same way that the lambda-calculus corresponds to natural deduction. Starting from natural deduction for the conjunction-implication fragment of intuitionistic logic we design a corresponding deep inference system together with reduction rules on proofs that allow a fine-grained… (More)

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs.… (More)

- Richard McKinley
- 2009

This paper is a brief intoduction to the αǫ-calculus – a calculus of communication and duplication inspired by the structure of the classical quantifiers. We will summarize the results of a paper in preparation on connections between extensions of the calculus, sequent sys-tems/proof nets for classical logic, and Herbrand's theorem.

- Richard McKinley
- 2005

While ideally noise should be reduced at the source, in the military environment the most effective solution in terms of both cost and operational effectiveness has been to provide personnel with personal hearing protection. This protection may be in the form of either an earplug that occludes the ear canal or a circumaural protector that inserts a barrier… (More)

PURPOSE
To improve the efficiency of the labeling task in automatic quality control of MR spectroscopy imaging data.
METHODS
28'432 short and long echo time (TE) spectra (1.5 tesla; point resolved spectroscopy (PRESS); repetition time (TR)= 1,500 ms) from 18 different brain tumor patients were labeled by two experts as either accept or reject, depending… (More)

MRSI grids frequently show spectra with poor quality, mainly because of the high sensitivity of MRS to field inhomogeneities. These poor quality spectra are prone to quantification and/or interpretation errors that can have a significant impact on the clinical use of spectroscopic data. Therefore, quality control of the spectra should always precede their… (More)

- Alessio Guglielmi, Richard McKinley, Sorin Stratulat, Roberto Maieli, Sara Negri, Matthias Baaz +6 others
- 2013

THEME Formal proofs are becoming increasingly important in a number of domains in computer science and mathematics. The topic of the colloquium is structural proof theory, broadly construed. Some examples of relevant topics: List of talks (in presentation order)