TY - GEN

T1 - A measure of logical inference and its game theoretical applications

AU - Kaneko, Mamoru

AU - Suzuki, Nobu Yuki

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Classical Logic

KW - Game Theoretic Decision Making

KW - Gentzen-style Sequent calculus

KW - Intuitionistic Logic

UR - http://www.scopus.com/inward/record.url?scp=80054078965&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-24130-7_10

DO - 10.1007/978-3-642-24130-7_10

M3 - Conference contribution

AN - SCOPUS:80054078965

SN - 9783642241291

VL - 6953 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 139

EP - 150

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 3rd International Workshop on Logic, Rationality and Interaction, LORI 2011

Y2 - 10 October 2011 through 13 October 2011

ER -