### 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 language | English |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 139-150 |

Number of pages | 12 |

Volume | 6953 LNAI |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

Event | 3rd International Workshop on Logic, Rationality and Interaction, LORI 2011 - Guangzhou Duration: 2011 Oct 10 → 2011 Oct 13 |

### Publication series

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

Volume | 6953 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

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

City | Guangzhou |

Period | 11/10/10 → 11/10/13 |

### Fingerprint

### 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

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

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 -