J. Herbrand. Recherches sur la theorie de la demonstration.PhDthesis, Universite de Paris, 1930. Home/Search Document Not in Database Summary Related Articles Check |
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A simple proof of Parsons' theorem - Ferreira (1 citation) (Correct)
.... 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 entail that a quantifier free first order consequence of a universal ....
....convoluted, proof of Parsons theorem in [Sie85] The proof technique used in [Sie91] was foreshadowed by an argument in [Fer90] 6. More precisely, we need a version of the Propriete A of first order validities (of the form ###) introduced by Jacques Herbrand in chapter V of his thesis [Her30]. This is the version of Herbrand s theorem without the introduction of (so called) index functions. 7. A theory U admits definition by cases if, for any terms t 1 (u) t k 1 (u) and quantifier free formulas #1 (u) #k (u) there is a term t(u) such that . ....
Jacques Herbrand. Recherches sur la theorie de la demonstration. PhD thesis, Universite de Paris, 1930. The relevant chapter is the fifth, which is translated in van Heijenoort (1967).
Multiset Constraints and P Systems - Agostino Dovier Carla (Correct)
....on the solution of equality constraints, that is on the uni cation problem. We show how to implement both standard and extended uni cation (namely, multiset uni cation) algorithms using P systems. 5.1 Standard Uni cation We start from the classical rst order uni cation problem c.f. e.g. [15, 20, 1]. Let be a rst order signature and C, s 1 = t 1 s n = t n , be a constraint composed by conjunctions of equations (i.e. an equation system) The uni cation problem, in its decision version, consists in checking if there is a substitution (a function from the variables occurring in ....
....n j nil 2 ]g i O = 1 (i.e. the output membrane is the skin) R 1 and R 2 are the sets of evolution rules for multisets with kernels nil 1 and nil 2 , respectively, that implement the uni cation test. Evolution rules for R 2 are obtained from the non deterministic uni cation algorithm Unify [15, 20] and are shown in Figure 4. Actually, each rule is a metarule consisting of all its in nite possible instances. However, only a nite number of instances depending on C is needed, as explained below. R 1 , instead, is assumed to be empty in this case. Classical results on Herbrand s ....
J. Herbrand. Recherches sur la theorie de la demonstration. Master's thesis, Universite de Paris, 1930. Also in Ecrits logiques de Jacques Herbrand, PUF, Paris, 1968.
If ; ; =) A + then ; =) A. - If Then Proof (Correct)
....substitution or uni er exists, and if so, we can e ectively compute it in linear time. Moreover, we can do so with a minimal commitment and we do not need to choose between various possible uni ers. Because of its central importance, uni cation has been thoroughly investigated. Herbrand [Her30] is given credit for the rst description of a uni cation algorithm in a footnote of his thesis, but it was not until 1965 that it was introduced into automated deduction through the seminal work by Alan Robinson [Rob65, Rob71] The rst algorithms were exponential, and later almost linear ....
Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
Multiset Constraints and P Systems - Dovier, Piazza, Rossi (Correct)
....the solution of equality constraints, that is on the unification problem. We show how to implement both standard and extended unification (namely, multiset unification) algorithms using P systems. 5.1 Standard Unification We start from the classical first order unification problem c.f. e.g. [15, 20, 1]. Let # be a first order signature and C, s 1 = t 1 s n = t n , be a constraint composed by conjunctions of equations (i.e. an equation system) The unification problem, in its decision version, consists in checking if there is a substitution # (a function from the variables occurring in C to ....
....n = t n i = 1 (i.e. the output membrane is the skin) R 1 and R 2 are the sets of evolution rules for multisets with kernels nil 1 and nil 2 , respectively, that implement the unification test. Evolution rules for R 2 are obtained from the non deterministic unification algorithm Unify [15, 20] and are shown in Figure 4. Actually, each rule is a metarule consisting of all its infinite possible instances. However, only a finite number of instances depending on C is needed, as explained below. R 1 , instead, is assumed to be empty in this case. Classical results on Herbrand s ....
J. Herbrand. Recherches sur la theorie de la demonstration. Master's thesis, Universite de Paris, 1930. Also in Ecrits logiques de Jacques Herbrand, PUF, Paris, 1968.
On the EA-Style Integrated Processing of Self-Contained.. - Degtyarev, Lyaletski (2000) (Correct)
....complex intellectual processes became feasible. As a response to the emergence of computing machinery of that sort a series of papers appeared in which the issues of the implementation of Gentzen type calculi [9] and inference search methods relying on the results of Skolem [10] and Herbrand [11] were discussed. For more detail, the reader is referred to, for example, 12] 13] 14] 15] etc. It might be well to point out that in those first papers an answer to the principal question about a possibility to use computers for mathematical reasoning was provided. But the lack of ....
Herbrand, J. Recherches sur la Theorie de la Demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovie, Class III, Sciences Mathematiques et Physiques (1930) Vol. 33. 16
Exploring the Behaviour of Feature Interaction via Stable Models - Accorsi (1999) (Correct)
....computational applications. There are methods supporting the implementation of this paradigm. Below we outline the transition from theory to computation. One of the basic constructions behind the current automated deduction and logic programming is the uni cation algorithm, devised by Herbrand [13]. The uni cation algorithm is responsible for assigning values to variables by means of automatically generated substitutions. These substitutions are called most general uni ers and the process of applying the substitutions to a program is called uni cation. Another fundamental construction ....
J. Herbrand. Recherches sur la theorie de la demonstrations. PhD thesis, Paris, 1930.
Completeness of Propositional Logic as a Program - Stansifer (2000) (Correct)
....and , then . Lemma 11 For any propositional formulas and , Lemma 12 If . then . Lemma 13 If and , then . 6 3. 4 The Deduction Theorem The first version of the deduction theorem appeared in Herbrand s thesis [4]. It is a considerable breakthrough in theorem construction technique. But it requires that the notation of a proof be enlarged to include proofs using assumptions, hence that surprising extra constructor in the proof data type. The theorem shows how to eliminate an assumption and provides another ....
Jacques Herbrand. Recherches sur la th eorie de la d emonstration. PhD thesis, Universit e de Paris, Paris, France, 1930. Translation of Chapter 5 appears in [14].
On Herbrand's Theorem - Samuel Buss University (1995) (6 citations) Self-citation (Herbrand) (Correct)
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J. Herbrand, Recherches sur la theorie de la demonstration, PhD thesis, University of Paris, 1930. Herbrand [9, p.552]
On Herbrand's Theorem - Samuel Buss University (1995) (6 citations) Self-citation (Herbrand) (Correct)
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J. Herbrand, Recherches sur la th#eorie de la d#emonstration, PhD thesis, UniversityofParis, 1930. Herbrand #9, p.552#
A Hidden Herbrand Theorem: Combining the Object and Logic.. - Goguen, Malcolm, Kemp Self-citation (Herbrand) (Correct)
....equalities serve as constraints on the possible values for logical variables in the set X . A solution to such a query in an algebra A consists of values in A for each variable (some of which may range over states) such that each equation is behaviorally satisfied. The classical Herbrand Theorem [41] says that for the models of a set of Horn clauses, existential queries can be answered by examining a particular term model, called the Herbrand universe (see [44, 1] for overviews of logic programming) This result was generalized to Horn clause logic with equality by Goguen and Meseguer [34, ....
Jacques Herbrand. Recherches sur la th'eorie de la d'emonstration. Travaux de la Soci'et'e des Sciences et des Lettres de Varsovie, Classe III, 33(128), 1930.
A First Order System with Finite Choice of Premises - Brünnler, Guglielmi (2004) (Correct)
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J. Herbrand. Recherches sur la theorie de la demonstration.PhDthesis, Universite de Paris, 1930.
Strategies for Focusing Structure-Based Theorem Proving - Amir, McIlraith (2001) (Correct)
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Herbrand, J. (1930). Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovie, Classe III Sci. Math. Phys., 33.
Constraint Logic Programming - Copyright Fran Cois (Correct)
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J. Herbrand, Recherches sur la theorie de la demonstration, These de doctorat (1930.
Unknown - Labeled Deduction Starting (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
Unknown - Linear Type Theory (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
Hierarchical Contextual Reasoning - Autexier (2003) (Correct)
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Herbrand, Jacques. (1930). Recherches sur la th eorie de la d emonstration. Sci. Lett. Varsovie, Classes III sci. math. phys., 33.
Bounded Arithmetic and Propositional Proof Complexity - Buss (1995) (1 citation) (Correct)
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J. Herbrand, Recherches sur la theorie de la demonstration, PhD thesis, University of Paris, 1930.
Bounded Arithmetic, Proof Complexity and Two Papers of Parikh - Buss (2002) (Correct)
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J. Herbrand, Recherches sur la theorie de la demonstration, PhD thesis, University of Paris, 1930.
Completeness of Propositional Logic as a Program - Ryan Stansifer Department (2001) (Correct)
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Jacques Herbrand. Recherches sur la th eorie de la d emonstration. PhD thesis, Universite de Paris, Paris, France, 1930. Translation of Chapter 5 appears in [17] pages 525--581.
Unknown - Linear Logic Programming (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
Unknown - Linear Type Theory (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
Unknown - Linear Calculus In (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
For the Completness Direction We Need to Generalize the.. - Theorem Completeness Of (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
Linear Type Checking - The Typing Rules (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
Termination - As The Example (Correct)
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Jacques Herbrand. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et de Lettres de Varsovic, 33, 1930.
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