Formalization of proofs using relational calculus

Yoshihiro Mizoguchi, Hisaharu Tanaka, Shuichi Inokuchi

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

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 languageEnglish
Title of host publicationProceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages527-531
Number of pages5
ISBN (Electronic)9784885523090
Publication statusPublished - Feb 2 2017
Event3rd International Symposium on Information Theory and Its Applications, ISITA 2016 - Monterey, United States
Duration: Oct 30 2016Nov 2 2016

Publication series

NameProceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016

Other

Other3rd International Symposium on Information Theory and Its Applications, ISITA 2016
CountryUnited States
CityMonterey
Period10/30/1611/2/16

Fingerprint

formalization
Automata theory
Computer science
computer science
assistant
tactics
coding
mathematics

All Science Journal Classification (ASJC) codes

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

Cite this

Mizoguchi, Y., Tanaka, H., & Inokuchi, S. (2017). Formalization of proofs using relational calculus. In 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.

Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016. Institute of Electrical and Electronics Engineers Inc., 2017. p. 527-531 7840480 (Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016).

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

Mizoguchi, Y, Tanaka, H & Inokuchi, S 2017, Formalization of proofs using relational calculus. in 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.
Mizoguchi Y, Tanaka H, Inokuchi S. Formalization of proofs using relational calculus. In Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016. Institute of Electrical and Electronics Engineers Inc. 2017. p. 527-531. 7840480. (Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016).
Mizoguchi, Yoshihiro ; Tanaka, Hisaharu ; Inokuchi, Shuichi. / Formalization of proofs using relational calculus. Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 527-531 (Proceedings of 2016 International Symposium on Information Theory and Its Applications, ISITA 2016).
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