J. Herbrand. Investigations in proof theory. In J. van Heijenoort, editor, From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931, pages 525-581. Harvard University Press, 1967.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is outweighed by the ease with which cut free sequent calculi can be mechanized. The next level of nondeterminism is in the guessing of the term instantiating an existential quanti er. By employing Herbrand functions and uni cation, this guesswork can be eliminated. The Herbrand theorem [6] states that a formula A of rst order logic can be transformed into a quanti er free formula AH such that A is provable if and only if some nite disjunction of instances of AH can be proved in classical propositional logic. The Herbrand theorem yields an e ective semi decision procedure for ....

J. Herbrand. Investigations in proof theory. In J. van Heijenoort, editor, From Frege to Godel: A Sourcebook of Mathematical Logic, 1879-1931.

....quantifiers from formulas so that one need only consider universally quantified formulas. Both of these developments are made use of in logic programming, where the Herbrand Universe is a major focus and programs are assumed to be written without existential quantifiers. In 1930, Herbrand [Her30] showed that the provability of an arbitrary formula in the predicate calculus can be reduced to the provability of a ground instance. Note: Herbrand independently came upon the domain originally described by Skolem, and the mistaken perception that Herbrand originated this domain led to its ....

....one inference scheme, known as resolution. Resolution, a mechanical step for combining two clauses to produce (infer) a third, provided for a straightforward yet powerful machineoriented method of deduction. A key component of resolution is unification, the process originally described by Herbrand [Her30] and extolled by Prawitz [Pra60] in the early 1960 s. Using unification to control the search for relevant clause instances, the resolution procedure was able to outperform other theorem proving procedures. Following the publication of Robinson s work, many refinements of resolution were devised, ....

J. Herbrand. Investigations in proof theory. 1930. English translation in [vH67].

....for the cut free fragment of LK. 1.2 Quantifiers and non classical logics The addition of quantifiers to CPL to form the predicate calculus (CPC) brings problems with non invertible rules (eigenvariable conditions) and the consequent limitation on the permutation congruence. Herbrand s Theorem [9], Gentzen s Mid Sequent Theorem [6] Smullyan s Fundamental Theorem [31] and the Prenex Normal Form Theorem, can be used to limit the impact of the non invertible rules and to retain the structure of the propositional search space. The cost is the superposition of the unification search space and ....

J. Herbrand. Investigations in proof theory. In: J. van Heijenoort (editor), From Frege to Godel , Harvard University Press, 1967.

....The present paper demonstrates that the above classical sequent based method can be adapted for theorem proving in the intuitionistic predicate calculus. The modifications require a careful proof theoretic analysis of the role of Herbrand functions and variables, and of unification in proof search [Her67]. The crucial aspect of our proof theoretic approach is the observation that Herbrand functions along with unification, serve to enforce the eigenvariable conditions on a sequent calculus derivation. The approach of Herbrandizing the goal formula prior to proof search does not work for ....

J. Herbrand. Investigations in proof theory. In J. van Heijenoort, editor, From Frege to Godel: A Source Book of Mathematical Logic, pages 525--581. Harvard University Press, Cambridge, Mass., 1967.

....abstraction into account. It is somewhat simpler than other systems for the same purpose that have previously appeared. 1 Introduction In classical logic, Herbrand s famous theorem of 1930 plays many roles. Herbrand seems to have thought of it as something like a constructive completeness theorem [12, 13]. Robinson cited it as the foundation of automated theorem proving [15] It has been applied to derive results on decidability [3] But despite its fundamental nature, it has remained remarkably classical. Completeness results, with suitable generalizations of Tarskian semantics, have been ....

Jacques Herbrand. Investigations in proof theory. 1930. English translation in [18].

....Dept. Mathematics and Computer Science Lehman College (CUNY) Bronx, NY 10468 Depts. Computer Science, Philosophy, Mathematics Graduate Center (CUNY) 33 West 42nd Street, NYC, NY 10036 August 16, 1996 1 Introduction Herbrand s theorem is a central fact about classical logic, [9, 10]. It provides a constructive method for associating, with each first order formula X, a sequence of formulas X 1 , X 2 , X 3 , so that X has a first order proof if and only if some X i is a tautology. Herbrand s theorem serves as a constructive alternative to Godel s completeness theorem. It ....

J. Herbrand. Investigations in proof theory. 1930. English translation in

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J. Herbrand. Investigations in proof theory. In J. van Heijenoort, editor, From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931, pages 525-581. Harvard University Press, 1967.

No context found.

J. Herbrand. Investigations in proof theory. In J. van Heijenoort, editor, From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931, pages 525-581. Harvard University Press, 1967.

No context found.

J. Herbrand. Investigations in proof theory. In J. van Heijenoort, editor, From Frege to Godel: A Source Book of Mathematical Logic, pages 525-581. Harvard University Press, Cambridge, Mass., 1967.

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