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Coinductive predicates and final sequences in a fibration

  • ICHIRO HASUO (a1), TOSHIKI KATAOKA (a1) (a2) and KENTA CHO (a3)
Abstract

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.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
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