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Coinductive predicates and final sequences in a fibration

Published online by Cambridge University Press:  18 April 2017

ICHIRO HASUO ,
TOSHIKI KATAOKA  and
KENTA CHO
ICHIRO HASUO
Affiliation:
Department of Computer Science, The University of Tokyo, Tokyo 113-8656, Japan Email: ichiro@is.s.u-tokyo.ac.jp
TOSHIKI KATAOKA
Affiliation:
Department of Computer Science, The University of Tokyo, Tokyo 113-8656, Japan Email: ichiro@is.s.u-tokyo.ac.jp Research Fellow of Japan Society for the Promotion of Science, 5-3-1, Kouji-machi, Chiyoda-ku, Tokyo 102-0083, Japan Email: toshikik@is.s.u-tokyo.ac.jp
KENTA CHO
Affiliation:
Institute for Computing and Information Sciences, Radboud University, P.O.Box 9010, 6500 GL Nijmegen, the Netherlands Email: K.Cho@cs.ru.nl
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Abstract

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Coinductive predicates express persisting ‘safety’ specifications of transition systems. Previous observations by Hermida and Jacobs identify coinductive predicates as suitable final coalgebras in a fibration – a categorical abstraction of predicate logic. In this paper, we follow the spirit of a seminal work by Worrell and study final sequences in a fibration. Our main contribution is to identify some categorical ‘size restriction’ axioms that guarantee stabilization of final sequences after ω steps. In its course, we develop a relevant categorical infrastructure that relates fibrations and locally presentable categories, a combination that does not seem to be studied a lot. The genericity of our fibrational framework can be exploited for binary relations (i.e. the logic of ‘binary predicates’) for which a coinductive predicate is bisimilarity, constructive logics (where interests are growing in coinductive predicates) and logics for name-passing processes.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Issue 4 , April 2018 , pp. 562 - 611
Copyright
Copyright © Cambridge University Press 2017 

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