Add to ORKGWe show that the types of the witnesses in the Herbrand functional interpretation can be simplified, avoiding the use of “sets of functionals” in the interpretation of implication and universal quantification. This is done by presenting an alternative formulation of the Herbrand functional interpretation, which we show to be equivalent to the original presentation. As a result of this investigation we also strengthen the monotonicity property of the original presentation, and prove a monotonicity property for our alternative definition
The original version of Herbrand’s theorem [8] for first-order logic provided the theoretical underp...
Abstract. The higher-order types of Herbrand interpretations for databases arise often in practice w...
International audienceWe present a new Curry-Howard correspondence for classical first-order natural...
Carrying out a suggestion by Kreisel, we adapt Gödel's functional interpretation to ordinary first-o...
The purpose of this article is to present a parametrised functional interpretation. Depending on the...
We introduce a new typed combinatory calculus with a type constructor that, to each type σ, associat...
Recently, the second author, Briseid, and Safarik introduced nonstandard Dialectica, a functional in...
Skolemization and Herbrand theorems are obtained for first-order logics based on algebras with a com...
Abstract. A unified approach 1 to the construction of original forms of the famous Herbrand theorem ...
Herbrand's theorem, widely regarded as a cornerstone of proof theory, exposes some of the constructi...
Abstract. Knowledge-base systems must typically deal with imperfection in knowl-edge, in particular,...
International audienceHerbrand's theorem, widely regarded as a cornerstone of proof theory, exposes ...
AbstractWe present a functional interpretation of Peano arithmetic that uses Gödel’s computable func...
International audienceKrivine presented in [Kri10] a methodology to combine Cohen's forcing with the...
Intuitionistic first-order logic extended with a restricted form of Markov\u27s principle is constru...
The original version of Herbrand’s theorem [8] for first-order logic provided the theoretical underp...
Abstract. The higher-order types of Herbrand interpretations for databases arise often in practice w...
International audienceWe present a new Curry-Howard correspondence for classical first-order natural...
Carrying out a suggestion by Kreisel, we adapt Gödel's functional interpretation to ordinary first-o...
The purpose of this article is to present a parametrised functional interpretation. Depending on the...
We introduce a new typed combinatory calculus with a type constructor that, to each type σ, associat...
Recently, the second author, Briseid, and Safarik introduced nonstandard Dialectica, a functional in...
Skolemization and Herbrand theorems are obtained for first-order logics based on algebras with a com...
Abstract. A unified approach 1 to the construction of original forms of the famous Herbrand theorem ...
Herbrand's theorem, widely regarded as a cornerstone of proof theory, exposes some of the constructi...
Abstract. Knowledge-base systems must typically deal with imperfection in knowl-edge, in particular,...
International audienceHerbrand's theorem, widely regarded as a cornerstone of proof theory, exposes ...
AbstractWe present a functional interpretation of Peano arithmetic that uses Gödel’s computable func...
International audienceKrivine presented in [Kri10] a methodology to combine Cohen's forcing with the...
Intuitionistic first-order logic extended with a restricted form of Markov\u27s principle is constru...
The original version of Herbrand’s theorem [8] for first-order logic provided the theoretical underp...
Abstract. The higher-order types of Herbrand interpretations for databases arise often in practice w...
International audienceWe present a new Curry-Howard correspondence for classical first-order natural...