Proof Theory (Logic and Foundations)

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Linear Network 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, Ed http://iml.univ-mrs.fr/ldp/LINEAR/ Gödel's Incompleteness Theorems Open Encyclopedia entry. http://open-site.org/Science/Mathematics/Logic/Proof_Theory/G%C3%B6del's_Incompleteness_Theorems/ The Calculus of Structures The calculus of structures is a new proof theoretical formalism. It exploits a top-down symmetry of derivations made possible by deep inference. http://alessio.guglielmi.name/res/cos/index.html Mathematical Reasoning Group Research group based in Edinburgh, it is running on the interaction between logic, mathematics and informatics. Links to publications, homepages, reports. http://dream.dai.ed.ac.uk/ ProofTheory.ORG Basic material on proof theory and the home page of the only mailing list devoted to proof theory, with hundreds of experts. http://www.prooftheory.org/ Fast-growing Functions and Unprovable Theorems Online seminar on Goodstein's Theorem, transfinite ordinals, formal number theory, Wainer Hierarchy of fast-growing functions, and the Kirby-Paris Theorem. http://www.maths.bris.ac.uk/~maadb/research/seminars/online/fgfut/fgfut09.html Proof Theory on the Eve of Year 2000 A survey consisting of 10 questions asked by Solomon Feferman and 29 responses. http://www-logic.stanford.edu/proofsurvey.html G. Japaridze's Papers Full list of publications by this author, with about 30 items in the area of proof theory. Many of the papers are downloadable. http://www.csc.villanova.edu/~japaridz/study.html Topics in Logic and Proof Theory Brief introductions to combinatory logic, the incompleteness theorems and independence results, by Andrew D Burbanks. http://www.maths.bris.ac.uk/~maadb/research/topics/logic/ Frogs Discussion Group Internet forum focused on the calculus of structures. http://news.gmane.org/group/gmane.science.mathematics.frogs/ Proof Theory Open Encyclopedia entry. Hierarchically organized by subtopics. http://open-site.org/Science/Mathematics/Logic/Proof_Theory/ The Epsilon Calculus Discussion of David Hilbert's development of this type of logical formalism with emphasis on proof-theoretic methods. http://plato.stanford.edu/entries/epsilon-calculus/ Proof Theory as an Alternative to Model Theory Short article by Dale Miller, arguing that logic programming languages should base their semantics on proof theory, not model theory. http://www-lp.doc.ic.ac.uk/UserPages/staff/ft/alp/comment/proof.html Logic of programming 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) http://iml.univ-mrs.fr/ldp/welcome.html

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