This paper presents a measure of inference in classical and intuitionistic logics in the Gentzen-style sequent calculus. The definition of the measure takes two steps: First, we measure the width of a given proof. Then the measure of inference assigns, to a given sequent, the minimum value of the widths of its possible proofs. It counts the indispensable cases for possible proofs of a sequent. This measure expresses the degree of difficulty in proving a given sequent. Although our problem is highly proof-theoretic, we are motivated by some general and specific problems in game theory/economics. In this paper, we will define a certain lower bound function, with which we may often obtain the exact value of the measure for a given sequent. We apply our theory a few game theoretical problems and calculate the exact values of the measure. © 2011 Springer-Verlag.
CITATION STYLE
Kaneko, M., & Suzuki, N. Y. (2011). A measure of logical inference and its game theoretical applications. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6953 LNAI, pp. 139–150). https://doi.org/10.1007/978-3-642-24130-7_10
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