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- Richard McKinley
- ACM Trans. Comput. Log.
- 2013

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)

- Richard McKinley
- LPAR
- 2010

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)

- Kai Brünnler, Richard McKinley
- LPAR
- 2008

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)

- Richard McKinley, Rik Wepfer, +4 authors Mauricio Reyes
- BrainLes@MICCAI
- 2016

- Richard McKinley
- Ann. Pure Appl. Logic
- 2013

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)

- Richard McKinley
- 2007

Herbrand's theorem is often presented as a corollary of Gentzen's sharpened Hauptsatz for the classical sequent calculus. However, the midsequent gives Herbrand's theorem directly only for formulae in prenex normal form. In the Handbook of Proof Theory, Buss claims to give a proof of the full statement of the theorem, using sequent calculus methods to show… (More)

- Richard McKinley
- J. Log. Algebr. Program.
- 2008

A formulation of naive set theory is given in Lafont's Soft Linear Logic, a logic with polynomial time cut-elimination. We demonstrate that the provably total functions of this set theory are precisely the PTIME functions. A novelty of this approach is the representation of the unary/binary natural numbers by two distinct sets (the safe naturals and the… (More)

- Alessio Guglielmi, Richard McKinley, +9 authors Luís Pinto
- 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)