Samuel R. Buss. On herbrand's theorem. In Logic and Computational Complexity, volume 960 of Lecture Notes in Computer Science, pages 195--209. Springer-Verlag, 1995. Home/Search Document Details and Download
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A simple proof of Parsons' theorem - Ferreira (1 citation) (Correct)
....can also proved through the analysis of a suitable complete proof system. The theorem is a simple consequence of Gentzen s verscharfter Hauptsatz, known in English as Gentzen s midsequent theorem (see [TS00] for this route) It can also be proved using Gentzen s plain Hauptsatz, as Buss does in [Bus95]. Herbrand s own method appears in his doctoral dissertation [Her30] The reader can find a partial translation into English of Herbrand s thesis in the volume [vHe67] together with commentaries and corrections of Herbrand s proof. Both analyses (a la Herbrand or a la Gentzen) automatically ....
Samuel Buss. On Herbrand's theorem. In Daniel Leivant, editor, Logic and Computational Complexity, volume 960 of Lecture Notes in Computer Science, pages 195--209. Springer-Verlag, 1995.
Proof Interpretations and the Computational Content of Proofs - Kohlenbach (2002) (1 citation) (Correct)
....# #x#y(fxy = 0) uniformly as a functional in f and the index functions. CHAPTER 1. UNWINDING PROOFS: PROOF MINING 17 Suggested further reading 1) On the general program of unwinding proofs (proof mining) 95] 96] 97] 35] 103] 30] 7] 40] 74] 79] 84] 2) On Herbrand s theorem: [23], 40] 70] 113] 95] 102] 3) On the no counterexample interpretation: 40] 82] 90] 91] 119] 120] 111] For other approaches to proof mining not treated in these notes see [26] and [27] Chapter 2 Intuitionistic logic and arithmetic in all finite types In the following we formulate an ....
Buss, S.R., On Herbrand's Theorem. In: Logic and Computational Complexity (Leivant, D., ed.), pp. 195-209. Springer LNCS 960 (1995).
Proof Mining in Analysis: Computability and Complexity - Oliva (2001) (Correct)
.... the Gdel number of that computation) The predicate T (x, y, z) is decidable (even primitive recursive) and the predicate T # (x) #yT (x, x, y) is undecidable (but recursively enumerable) The material of the following section on Proof Mining is substantially based on [AF98] BS95] BSBar] [Bus95], Koh98a] Koh93a] Tro73] and [Tv88] 4 2 Proof Mining The general purpose of Proof Mining is to extract from a given proof of a formula A in a system A some constructive content. By constructive content we normally mean a realizing term for the existential quantifiers of A. For ....
....of A. Example: Take the sentence used above, A : #x(#yT (x, x, y) ##zT (x, x, z) Let us consider the following prenex form of A, A p : #x#y#z(T (x, x, y) # T (x, x, z) 7 For a general statement of the theorem see [Koh98a] and for a detailed exposition about Herbrand s work see [Bus95]. 6 The Herbrand normal form of A p would be, A H p : #y(T (f 0 , f 0 , y) # T (f 0 , f 0 , f 1 (y) Since A p can be proved in PL we are guaranteed by the Soundness of H translation that terms t 1 , t n can be extracted from the proof PL # A p such that, A H,D p : n # ....
S. R. Buss. On Herbrand's theorem. In D. Leivant, editor, Logic and Computational Complexity, Lecture Notes in Computer Science, volume 960, pages 195--209. Springer Verlag, 1995.
On Herbrand Skeletons - Voda, Komara (1995) (1 citation) (Correct)
....does not contain the identity : then for any skeleton of size n the conversion procedure yields a finite number of unification problems (i.e. m = 0 in each of the problems) Hence, Sk n ( restricted to such existential formulas is decidable. This has been also known to Herbrand, see also [Bus95a, Bus95b]. 3.6 Converting Herbrand skeletons to SREU problems. In this paragraph we reduce in the following sense the problem of solvability of Herbrand skeletons to a class of SREU problems: To every quantifier free formula OE( we can primitively recursively find a finite class Gamma of SREU problems ....
S. R. Buss. On Herbrand's theorem. Typeset manuscript, to appear in Proceedings of LCC'95, 1995.
Cut Elimination inside a Deep Inference System for Classical.. - Brünnler (2002) (Correct)
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Samuel R. Buss. On herbrand's theorem. In Logic and Computational Complexity, volume 960 of Lecture Notes in Computer Science, pages 195--209. Springer-Verlag, 1995.
Cut Elimination inside a Deep Inference System for Classical.. - Brünnler (2005) (Correct)
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Samuel R. Buss. On herbrand's theorem. In Logic and Computational Complexity, volume 960 of Lecture Notes in Computer Science, pages 195--209. Springer-Verlag, 1995.
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