Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Handbook of Automated Reasoning: Volume 1
Handbook of Automated Reasoning: Volume 1
System for Automated Deduction (SAD): Linguistic and Deductive Peculiarities
Proceedings of the IIS'2002 Symposium on Intelligent Information Systems
Evidence algorithm and system for automated deduction: a retrospective view
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
On herbrand's theorem for intuitionistic logic
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
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New sequent forms* of the famous Herbrand theorem are proved for first-order classical logic without equality. These forms use the original notion of an admissible substitution and a certain modification of the Herbrand universe, which is constructed from constants, special variables, and functional symbols occurring only in the signature of an initial theory. Other well-known forms of the Herbrand theorem are obtained as special cases of the sequent ones. Besides, the sequent forms give an approach to the construction and theoretical investigation of computer-oriented calculi for efficient logical inference search in the signature of an initial theory. In a comparably simple way, they provide us with some technique for proving the completeness and soundness of the calculi.