Jean-Yves Girard. Proof Theory and Logical Complexity, volume 1 of Studies in Proof Theory. Bibliopolis, 1987. Home/Search Document Not in Database Summary Related Articles Check |
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A Local System for Classical Logic - Brünnler, Tiu (2001) (51 citations) (Correct)
....for system SKS, but we have no syntactic proof inside the calculus of structures, i.e. without detour through the sequent calculus and without resorting to semantics. We are interested in such a proof because it can be modular, contrary to cut elimination proofs in the sequent calculus, cf. Girard [4] p.15. This modularity stems from the fact that due to atomicity of the cut, cut elimination in the calculus of structures is not a nested induction taking into account the cut rank; instead it is based on a number of lemmas about permutability of rules wrt. one another (for a rather general ....
Jean-Yves Girard. Proof Theory and Logical Complexity, Volume I, volume 1 of Studies in Proof Theory. Bibliopolis, Napoli, 1987. Distributed by Elsevier.
Looking From the Inside and From the Outside - Carbone, Semmes (1998) (Correct)
....to code mathematical constructions into formal proofs and therefore as a tool for measuring information content in new ways. Note that implicit descriptions of constructions provided by proofs with lemmas can be converted into explicit constructions through the procedure of cut elimination [21, 45, 10], but this can lead to large expansion. The general idea of feasibility can be applied to finitely generated groups (as in Section 6 below) Again we think of the length of the shortest proof of the feasibility of an element of the group as a measurement of its information content. This case ....
....an explicit construction of the term t. With the cut rule one can make short proofs of feasibility which provide only implicit descriptions, as we shall soon see. There are effective methods for converting proofs with cuts into proofs without, at the cost of great expansion in the proofs. See [21, 45, 10]. Let us mention one more point. In [36] an F : inequality rule is included in the axioms, to the effect that if y is feasible and x y then x is also feasible. For the historical concern about large numbers this is a reasonable requirement to consider, but we have omitted it intentionally. It ....
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J.-Y. Girard. Proof Theory and Logical Complexity. volume 1 of Studies in Proof Theory, Monographs -- Bibliopolis, Napoli, Italy, 1987.
Asymptotic Cyclic Expansion and Bridge Groups of Formal Proofs - Carbone (2000) (2 citations) (Correct)
....Gentzen Cut Elimination Theorem [Gen34] to the effect that the rule of modus ponens is not needed in some logical systems, that is, one can make proofs without using lemmas. The strength of this result is forcefully manifested by Girard who, by applying Gentzen s Cut Elimination Theorem, shows [Gir87a] that one can recover the elementary combinatorial argument used by van der Waerden to prove his theorem on arithmetic progressions 1 [VdW27] from the transcendental methods in dynamical systems used by Furstenberg and Weiss [FW78] In other words, the convoluted combinatorial proof of van der ....
....In the following we think of proofs as formalized in the sequent calculus where the cut rule plays the role of modus ponens. We shall introduce these notions and give some insights in Section 2. For a full presentation of the sequent calculus and the Gentzen s Cut Elimination theorem, see [Gir87a, Tak87]. In Section 2.1 we present some logical construction of large numbers in arithmetic and in Section 3 we recall the notion of distortion in groups. The notions of logical graph and cycles in proofs will be recalled in 4 Section 4 and in Section 4.1 we describe how cycles are formed in the two ....
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J.Y. Girard. Proof Theory and Logical Complexity. volume 1 of Studies in Proof Theory, Monographs -- Bibliopolis, Napoli, Italy, 1987. 39
System Description: CutRes 0.1: Cut Elimination by Resolution - Baaz, Leitsch, .Moser (Correct)
.... Institut f. Algebra und Computermathematik, E118.2, Technische Universitat Wien, Wiedner Hauptstrasse 8 10, A 1040 Vienna, Austria, fbaaz,moserg logic.at Institut f. Computersprachen, E185.2, Technische Universitat Wien, Resselgasse 3, A 1040 Vienna, Austria, leitsch logic.at cases [Gen34,Her71,Gir87], c.f. the analysis of van der Waerden s Theorem by Girard [Gir87] In this paper we present a method of cut elimination by resolution implemented as the system CutRes. We describe the current state of the system and intended extensions. The investigation of cut formulas and the impact of the ....
....Wien, Wiedner Hauptstrasse 8 10, A 1040 Vienna, Austria, fbaaz,moserg logic.at Institut f. Computersprachen, E185.2, Technische Universitat Wien, Resselgasse 3, A 1040 Vienna, Austria, leitsch logic.at cases [Gen34,Her71,Gir87] c.f. the analysis of van der Waerden s Theorem by Girard [Gir87]. In this paper we present a method of cut elimination by resolution implemented as the system CutRes. We describe the current state of the system and intended extensions. The investigation of cut formulas and the impact of the syntax of cuts to cut elimination and proof complexity have received ....
J. Y. Girard. Proof Theory and Logical Complexity, volume 1 of Studies in Proof Theory, Monographs. Bibliopolis, Napoli, Italy, 1987.
Sequentiality by Linear Implication and Universal Quantification - Guglielmi (1995) (3 citations) (Correct)
....from the result in [10] and the cut elimination theorem. 2.2.1 Theorem A sequent (M j h 1 ; M) has a proof in Forum O Gammaffi8 iff ( M 1 Gammaffi Delta Delta Delta Gammaffi M h Gammaffi M) has a proof in linear logic. Treating eigenvariables in 8 R as quantified variables (cfr. [6]) substitutions can be extended to derivations in a way that the following result holds. This is crucial for the proof search as computation framework. 2.2.2 Theorem For every oe, if Delta 2 Forum O Gammaffi8 then Deltaoe 2 Forum O Gammaffi8 . 3 Syntax and Operational Semantics of SMR ....
J.-Y. Girard. Proof Theory and Logical Complexity, Volume I, volume 1 of Studies in Proof Theory. Bibliopolis, Napoli, 1987. Distributed by Elsevier.
Turning Cycles into Spirals - Carbone (1999) (1 citation) Self-citation (Logical) (Correct)
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J.Y. Girard. Proof Theory and Logical Complexity, volume 1 of Studies in Proof Theory, Monographs. Bibliopolis, 1987.
A Formal Calculus for Categories - Caccamo (2003) (Correct)
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Jean-Yves Girard. Proof Theory and Logical Complexity, volume 1 of Studies in Proof Theory. Bibliopolis, 1987.
A Formal Calculus for Categories - Caccamo (2003) (Correct)
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Jean-Yves Girard. Proof Theory and Logical Complexity, volume 1 of Studies in Proof Theory. Bibliopolis, 1987.
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