论文信息 - On Admissible Substitutions in Classical and Intuitionistic Sequent Logics

On Admissible Substitutions in Classical and Intuitionistic Sequent Logics

In this paper the special notions of admissible substitutions are defined in order to reach higher efficiency of sequent inference search in Gentzen’s classical and intuitionistic calculi LK and LJ. These notions concern with a certain quantifier manipulation both in LK and in LJ. As a result, they lead to the construction of efficient modifications of calculi LK and LJ differed only by the notions of admissibility and having special technique for optimizing quantifier riles applications. This play a special role for LJ because using analog of skolemization for LJ requires sophistical technique of formulas transformation. Some results about the modifications of the calculi LK and LJ are given. A special example illustrates the different ways of applying the notions of admissibility.

Alexander V. Lyaletski

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