Francesco Dagnino - Foundations of regular coinduction

lmcs:6553 - Logical Methods in Computer Science, October 1, 2021, Volume 17, Issue 4 -
Foundations of regular coinductionArticle

Authors: Francesco Dagnino

    Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a middle way interpretation, called regular, which combines advantages of both approaches: it allows non-well-founded reasoning while being finite. We show that the natural proof-theoretic definition of the regular interpretation, based on regular trees, coincides with a rational fixed point. Then, we provide an equivalent inductive characterization, which leads to an algorithm which looks for a regular derivation of a judgment. Relying on these results, we define proof techniques for regular reasoning: the regular coinduction principle, to prove completeness, and an inductive technique to prove soundness, based on the inductive characterization of the regular interpretation. Finally, we show the regular approach can be smoothly extended to inference systems with corules, a recently introduced, generalised framework, which allows one to refine the coinductive interpretation, proving that also this flexible regular interpretation admits an equivalent inductive characterisation.

    Volume: Volume 17, Issue 4
    Published on: October 1, 2021
    Accepted on: May 11, 2021
    Submitted on: June 12, 2020
    Keywords: Computer Science - Logic in Computer Science


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