Theoretical Computer Science
Proofs and types
Normalization theorems for full first order classical natural deduction
Journal of Symbolic Logic
Computational interpretations of linear logic
Theoretical Computer Science - Special volume of selected papers of the Sixth Workshop on the Mathematical Foundations of Programming Semantics, Kingston, Ont., Canada, May 1990
MFPS '92 Selected papers of the conference on Meeting on the mathematical foundations of programming semantics, part I : linear logic: linear logic
On the &pgr;-calculus and linear logic
MFPS '92 Selected papers of the conference on Meeting on the mathematical foundations of programming semantics, part I : linear logic: linear logic
Interaction categories and communicating sequential processes
A classical mind
Proceedings of the workshop on Advances in linear logic
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Graphic Apology for Symmetry and Implicitness
Graphic Apology for Symmetry and Implicitness
Geometry of interaction 2: deadlock-free algorithms
COLOG '88 Proceedings of the International Conference on Computer Logic
NP-Completeness: A Retrospective
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
On the lengths of proofs in the propositional calculus (Preliminary Version)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Mechanizing proof theory: resource-aware logics and proof-transformations to extract implicit information
Towards Hilbert's 24th Problem: Combinatorial Proof Invariants
Electronic Notes in Theoretical Computer Science (ENTCS)
Proof-graphs: a Thorough Cycle Treatment, Normalization and Subformula Property
Fundamenta Informaticae - Logic, Language, Information and Computation
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We are here concerned with the study of proofs from a geometric perspective. By first recalling the pioneering work of Statman in his doctoral thesis Structural Complexity of Proofs (1974), we review two recent research programmes which approach the study of structural properties of formal proofs from a geometric perspective: (i) the notion of proof-net, given by Girard in 1987 in the context of linear logic; and (ii) the notion of logical flow graph given by Buss in 1991 and used as a tool for studying the exponential blow up of proof sizes caused by the cut-elimination process, a recent programme (1996-2000) proposed by Carbone in collaboration with Semmes.Statman's geometric perspective does not seem to have developed much further than his doctoral thesis, but the fact is that it looks as if the main idea, i.e. extracting structural properties of proofs in natural deduction (ND) using appropriate geometric intuitions, offers itself as a very promising one. With this in mind, and having at our disposal some interesting and rather novel techniques developed for proof-nets and logical flow graphs, we have tried to focus our investigation on a research for an alternative proposal for looking at the geometry of ND systems. The lack of symmetry in ND presents a challenge for such a kind of study. Of course, the obvious alternative is to look at multiple-conclusion calculi. We already have in the literature different approaches involving such calculi. For example, Kneale's (1958) tables of development (studied in depth by Shoesmith & Smiley (1978)) and Ungar's (1992) multiple-conclusion ND.After surveying the main research programmes, we sketch a proposal which is similar to both Kneale's and Ungar's in various aspects, mainly in the presentation of a multiple conclusion calculus in ND style. Rather than just presenting yet another ND proof system, we emphasise the use of 'modern' graph-theoretic techniques in tackling the 'old' problem of adequacy of multiple-conclusion ND. Some of the techniques have been developed for proof-nets (e.g. splitting theorem, soundness criteria, sequentialisation), and have proved themselves rather elegant and useful indeed.