HERBRAND THEOREMS: THE CLASSICAL AND INTUITIONISTIC CASES

A unified approach is applied for the construction of sequent forms of the famous Herbrand theorem for first-order classical and intuitionistic logics without equality. The forms do not explore skolemization, have wording on deducibility, and as usual, provide a reduction of deducibility in the first-order logics to deducibility in their propositional fragments. They use the original notions of admis- sibility, compatibility, a Herbrand extension, and a Herbrand universe being constructed from constants, special variables, and functional symbols occurring in the signature of a formula under investigation. The ideas utilized in the research may be applied for the construction and theoretical investigations of various computer-oriented calculi for ecient logical inference search without skolemization in both classical and intuitionistic logics and provide some new technique for further development of methods for automated reasoning in non-classical logics.

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