By Klaus Aehlig, Jan Johannsen, Helmut Schwichtenberg (auth.), Reinhard Kahle, Peter Schroeder-Heister, Robert Stärk (eds.)
ISBN-10: 354042752X
ISBN-13: 9783540427520
Proof conception has lengthy been tested as a uncomplicated self-discipline of mathematical common sense. It has lately turn into more and more correct to computing device technology. The - ductive equipment supplied by way of facts concept has proved helpful for metatheoretical reasons in addition to for functional purposes. hence it appeared to us so much traditional to deliver researchers jointly to evaluate either the position facts idea already performs in laptop technology and the function it could play sooner or later. the shape of a Dagstuhl seminar is best suited for reasons like this, as Schloß Dagstuhl offers a truly handy and stimulating surroundings to - scuss new principles and advancements. To accompany the convention with a proc- dings quantity looked as if it would us both acceptable. this kind of quantity not just ?xes uncomplicated result of the topic and makes them to be had to a broader viewers, but additionally signs to the scienti?c neighborhood that evidence conception in laptop technology (PTCS) is a tremendous learn department in the wider ?eld of good judgment in computing device science.
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Additional info for Proof Theory in Computer Science: International Seminar, PTCS 2001 Dagstuhl Castle, Germany, October 7–12, 2001 Proceedings
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407-474, 1998 12. S. Troelstra and H. Schwichtenberg, Basic Proof Theory, Cambridge University Press, 1996. A Note on the Proof-Theoretic Strength of a Single Application of the Schema of Identity uller2 Matthias Baaz1 and Christian G. at Abstract. Every instance of the schema of identity is derivable from identity axioms. However, from a proof theoretic perspective the schema of identity is quite powerful. Even one instance of it can be used to prove formulas uniformly where no fixed number of instances of identity axioms is sufficient for this purpose.
H. Barendregt, “Lambda calculi with types”. , Oxford University Press, pp. 118-309, 1992 5. R. Constable, “Types in logic, mathematics and programming”. In Handbook in Proof Theory, S. , Elsevier, pp. 683-786, 1998 6. D. de Jongh and G. Japaridze, “Logic of Provability”, in S. , Handbook of Proof Theory, Elsevier, pp. 475-546, 1998 7. -Y. Girard, Y. Lafont, P. Taylor, Proofs and Types, Cambridge University Press, 1989. 8. N. Krupski, “Operational Logic of Proofs with Functionality Condition on Proof Predicate”, Lecture Notes in Computer Science, v.
Proof. Let r1p (0 + 0) ≡ [0]p+ + ([0]p−1 + . . + ([0]2+ + 0) . ) + where “(0 + 0)” in “r1p (0 + 0)” refers to all occurrences of subterms of this form. Let r2p (0 + 0) ≡ [0]p−1 + (. . + ([0]2+ + (0 + 0) . , the underlined) occurrence of 0 + 0. Note that r2p (0 + 0) ≡ r1p (0). The needed instance T of the transitivity axiom is (r1p (0 + 0) = r1p (0) ∧ r2p (0 + 0) = r2p (0)) ⊃ r1p (0 + 0) = r2p (0). Let and tp1 ≡ [0]p+ tp2 ≡ [0]p−1 + (. . + ([0]2+ + 0) . ). + Note that tp2 ≡ r2p (0) and tp1 + tp2 ≡ r1 (0 + 0); tp1 is identical to the parameter term and the conclusion of the instance of the transitivity axiom is identical to instance of the premise in x + y = y ⊃ x = 0.
Proof Theory in Computer Science: International Seminar, PTCS 2001 Dagstuhl Castle, Germany, October 7–12, 2001 Proceedings by Klaus Aehlig, Jan Johannsen, Helmut Schwichtenberg (auth.), Reinhard Kahle, Peter Schroeder-Heister, Robert Stärk (eds.)
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