Quantifier Handling Issues in Computer-Oriented Intuitionistic Calculi

A new computer-oriented sequent calculus for 1st-order intuitionistic logic is described. The calculus demonstrates the possible method of the optimization of the procedure of quantifier rule applications in the inference search process. Our main objective is to show that by using the original notion of admissible substitutions, a computer-oriented logical inference technique can be created, which does not require analogs of the preliminary skolemization of formulas in intuitionistic logic and which has rather high inference search efficiency. Some results on the soundness and completeness of the calculus are given.