TY - GEN

T1 - Formalization of proofs using relational calculus

AU - Mizoguchi, Yoshihiro

AU - Tanaka, Hisaharu

AU - Inokuchi, Shuichi

N1 - Publisher Copyright:
© 2016 IEICE.

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.

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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.

T2 - 3rd International Symposium on Information Theory and Its Applications, ISITA 2016

Y2 - 30 October 2016 through 2 November 2016

ER -