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Lectures on Jacques Herbrand as a Logician

Wirth, Siekmann, Benzmueller & Autexier. Lectures on Jacques Herbrand as a Logician. SEKI Report SR-2009-01.

Herbrand's work, more than that of any other, provides the intellectual foundations of logic programming. This very readable article discusses Herbrands' contributions to proof theory and the formulation of the idea of a recursive function, and most importantly to PL, his fundamental theorem that yields a semi-decision algorithm for first-order logic and his unification algorithm.

By Charles Stewart at 2009-06-05 13:42 | Theory | other blogs | 6609 reads

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Herbrand Logic

This is an interesting and closely related paper: Herbrand Logic.

By Hank Thediek at Thu, 2009-06-11 02:37 | login or register to post comments

Is Herbrand Logic Herbrand's logic?

This article nicely summarises a thesis, that the interpretation of structures given in first-order logic into the structure's Herbrand universe is usually the best interpretation, which seems to be widespread in the theory of Prolog.

Pay attention to theorem 6: this thesis only makes sense with theories whose axioms are in Skolem normal form. This is quite hairy for theories with axiom schemas: eg. ZFC's axiom of replacement, so one usually wants to recast such theories into a higher-order theory with appropriate second-order variables to replace the schemas.

I'm guessing that Herbrand didn't actually advocate the thesis in this paper.

By Charles Stewart at Thu, 2009-06-11 13:22 | login or register to post comments

Herbrand's Logic?

I'm guessing that Herbrand didn't actually advocate the thesis in this paper.

I am guessing that you are right. In the introduction the authors define Herbrand logic as first-order logic plus Herbrand semantics. This seems to be sufficiently different to require a new definition.
The introduction tells a story of how the paper came about and why.

By Hank Thediek at Thu, 2009-06-11 17:42 | login or register to post comments