A measure of logical inference and its game theoretical applications

Mamoru Kaneko, Nobu Yuki Suzuki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages139-150
Number of pages12
Volume6953 LNAI
DOIs
Publication statusPublished - 2011
Externally publishedYes
Event3rd International Workshop on Logic, Rationality and Interaction, LORI 2011 - Guangzhou
Duration: 2011 Oct 102011 Oct 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6953 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other3rd International Workshop on Logic, Rationality and Interaction, LORI 2011
CityGuangzhou
Period11/10/1011/10/13

Fingerprint

Game theory
Game
Economics
Sequent Calculus
Intuitionistic Logic
Classical Logic
Game Theory
Assign
Count
Express
Lower bound
Calculate

Keywords

  • Classical Logic
  • Game Theoretic Decision Making
  • Gentzen-style Sequent calculus
  • Intuitionistic Logic

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

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). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6953 LNAI). https://doi.org/10.1007/978-3-642-24130-7_10

A measure of logical inference and its game theoretical applications. / Kaneko, Mamoru; Suzuki, Nobu Yuki.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6953 LNAI 2011. p. 139-150 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6953 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kaneko, M & Suzuki, NY 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, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6953 LNAI, pp. 139-150, 3rd International Workshop on Logic, Rationality and Interaction, LORI 2011, Guangzhou, 11/10/10. https://doi.org/10.1007/978-3-642-24130-7_10
Kaneko M, Suzuki NY. 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. 2011. p. 139-150. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-24130-7_10
Kaneko, Mamoru ; Suzuki, Nobu Yuki. / A measure of logical inference and its game theoretical applications. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6953 LNAI 2011. pp. 139-150 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{cb52da32bbe54b0cb9cd7cfa2f948a92,
title = "A measure of logical inference and its game theoretical applications",
abstract = "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.",
keywords = "Classical Logic, Game Theoretic Decision Making, Gentzen-style Sequent calculus, Intuitionistic Logic",
author = "Mamoru Kaneko and Suzuki, {Nobu Yuki}",
year = "2011",
doi = "10.1007/978-3-642-24130-7_10",
language = "English",
isbn = "9783642241291",
volume = "6953 LNAI",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "139--150",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

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

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

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)

ER -