### Abstract

We introduce a theory of relations and a method to prove using relational calculus. Several notions in mathematics and computer science are formalized using relational expressions. Propositions described by relational expressions can be solved by relational calculus, symbolic computations. We propose to apply our formalization to proofs in coding theory especially formalizations of algorithms including an error-correcting algorithm using automata. We introduce a formalization of notions in category theory and automata theory using relational expressions. We also show a formalization of an elementary theory of relations in Coq, a proof assistant system. We introduce an automatic proving procedures (tactics) for our formalization of the theory of relational calculus.

Original language | English |
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Title of host publication | Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 527-531 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523090 |

Publication status | Published - Feb 2 2017 |

Event | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 - Monterey, United States Duration: Oct 30 2016 → Nov 2 2016 |

### Publication series

Name | Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016 |
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### Other

Other | 3rd International Symposium on Information Theory and Its Applications, ISITA 2016 |
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Country | United States |

City | Monterey |

Period | 10/30/16 → 11/2/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Hardware and Architecture
- Information Systems
- Signal Processing
- Library and Information Sciences

### Cite this

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016*(pp. 527-531). [7840480] (Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016). Institute of Electrical and Electronics Engineers Inc..

**Formalization of proofs using relational calculus.** / Mizoguchi, Yoshihiro; Tanaka, Hisaharu; Inokuchi, Shuichi.

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

*Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016.*, 7840480, Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016, Institute of Electrical and Electronics Engineers Inc., pp. 527-531, 3rd International Symposium on Information Theory and Its Applications, ISITA 2016, Monterey, United States, 10/30/16.

}

TY - GEN

T1 - Formalization of proofs using relational calculus

AU - Mizoguchi, Yoshihiro

AU - Tanaka, Hisaharu

AU - Inokuchi, Shuichi

PY - 2017/2/2

Y1 - 2017/2/2

N2 - We introduce a theory of relations and a method to prove using relational calculus. Several notions in mathematics and computer science are formalized using relational expressions. Propositions described by relational expressions can be solved by relational calculus, symbolic computations. We propose to apply our formalization to proofs in coding theory especially formalizations of algorithms including an error-correcting algorithm using automata. We introduce a formalization of notions in category theory and automata theory using relational expressions. We also show a formalization of an elementary theory of relations in Coq, a proof assistant system. We introduce an automatic proving procedures (tactics) for our formalization of the theory of relational calculus.

AB - We introduce a theory of relations and a method to prove using relational calculus. Several notions in mathematics and computer science are formalized using relational expressions. Propositions described by relational expressions can be solved by relational calculus, symbolic computations. We propose to apply our formalization to proofs in coding theory especially formalizations of algorithms including an error-correcting algorithm using automata. We introduce a formalization of notions in category theory and automata theory using relational expressions. We also show a formalization of an elementary theory of relations in Coq, a proof assistant system. We introduce an automatic proving procedures (tactics) for our formalization of the theory of relational calculus.

UR - http://www.scopus.com/inward/record.url?scp=85015180222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015180222&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85015180222

T3 - Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016

SP - 527

EP - 531

BT - Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -