J. Łoś, A. Mostowski, and H. Rasiowa. A proof of Herbrand's theorem. Journal de mathématiques pures et appliquées, Folge 9 Bd. 35 (1956), S. 19–24. - J. Łoś, H. Rasiowa, and A. Mostowski. Addition au travail “A proof of Herbrand theorem.”Journal de mathématiques pures et appliquées, Folge 9 Bd. 40 (1961), S. 129–134.

1971 ◽  
Vol 36 (1) ◽  
pp. 168-169
Author(s):  
Kurt Schütte
Keyword(s):  
Herbrand’S Theorem ◽  
Herbrand's Theorem ◽  
Herbrand Theorem

Algorithmic logic and its applications in the theory of programs I

1977 ◽  
Vol 1 (1) ◽  
pp. 1-17
Author(s):  
Grażyna Mirkowska
Keyword(s):  
Normal Form ◽  
Programming Language ◽  
Formal Proof ◽  
Herbrand’S Theorem ◽  
Algorithmic Logic ◽  
Herbrand's Theorem ◽  
Herbrand Theorem ◽  
Algorithmic Property

The paper presents tools for formalizing and proving properties of programs. The language of algorithmic logic constitutes an extension of a programming language by formulas that describe algorithmic properties. The paper contains two axiomatizations of algorithmic logic, which are complete. It can be proved that every valid algorithmic property possesses a formal proof. An analogue of Herbrand theorem and a theorem on the normal form of a program are proved. Results of meta-mathematical character are applied to theory of programs, e.g. Paterson’s theorem is an immediate corollary to Herbrand’s theorem.

Herbrand's Theorem for Nonstandard Inference Operations

1994 ◽  
Vol 4 (2) ◽  
pp. 143-156
Author(s):  
JÜRGEN DIX ◽  
MARTIN KUMMER
Keyword(s):  
Herbrand’S Theorem ◽  
Herbrand's Theorem

An Improvement of Herbrand's Theorem and Its Application to Model Generation Theorem Proving

2007 ◽  
Vol 22 (4) ◽  
pp. 541-553
Author(s):  
Yu-Yan Chao ◽  
Li-Feng He ◽  
Tsuyoshi Nakamura ◽  
Zheng-Hao Shi ◽  
Kenji Suzuki ◽  
...  
Keyword(s):  
Theorem Proving ◽  
Model Generation ◽  
Generation Theorem ◽  
Herbrand’S Theorem ◽  
Herbrand's Theorem ◽  
Model Generation Theorem Proving

scholarly journals Herbrand's theorem as higher order recursion

2020 ◽  
Vol 171 (6) ◽  
pp. 102792
Author(s):  
Bahareh Afshari ◽  
Stefan Hetzl ◽  
Graham E. Leigh
Keyword(s):  
Higher Order ◽  
Herbrand’S Theorem ◽  
Herbrand's Theorem
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