Mathematical Reasoning Group - http://dream.dai.ed.ac.uk/ Research group based in Edinburgh, it is running on the interaction between logic, mathematics and informatics. Links to publications, homepages, reports.
The Epsilon Calculus - http://plato.stanford.edu/entries/epsilon-calculus/ Discussion of David Hilbert's development of this type of logical formalism with emphasis on proof-theoretic methods.
G. Japaridze's Papers - http://www.csc.villanova.edu/~japaridz/study.html Full list of publications by this author, with about 30 items in the area of proof theory. Many of the papers are downloadable.
Proof Theory - http://open-site.org/Science/Mathematics/Logic/Proof_Theory/ Open Encyclopedia entry. Hierarchically organized by subtopics.
Proof Theory as an Alternative to Model Theory - http://www.lix.polytechnique.fr/Labo/Dale.Miller/papers/ProofTheoryAsAlternative.html Short article by Dale Miller, arguing that logic programming languages should base their semantics on proof theory, not model theory.
Logic of programming - http://iml.univ-mrs.fr/ldp/welcome.html The "Logic of Programming" research team is interested in proof theory and its relations with theoretical computer science. The main topic is mathematical interpretation of proofs : nets (proof = graph), denotational semantics (proof = function), and game semantics (proof = strategy). Two realisations of this working program are Linear Logic and Ludics.
Linear Network - http://iml.univ-mrs.fr/ldp/LINEAR/ Linear Logic in Computer Science is lead by the "Logic of Programming" research team. Its thematic is focused on developing the theory and the applications of Linear Logic. It is formed by seven sites located in Marseille, Bologna, Cambridge, Edinburgh, Lisboa, Paris and Roma, and a few subsites.
The Calculus of Structures - http://alessio.guglielmi.name/res/cos/index.html The calculus of structures is a new proof theoretical formalism. It exploits a top-down symmetry of derivations made possible by deep inference.
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