Francesco Dagnino - Coaxioms: flexible coinductive definitions by inference systems

lmcs:4745 - Logical Methods in Computer Science, February 20, 2020, Volume 15, Issue 1 -
Coaxioms: flexible coinductive definitions by inference systemsArticle

Authors: Francesco Dagnino

    We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which can only be applied "at infinite depth" in a proof tree. Coaxioms allow us to interpret recursive definitions as fixed points which are not necessarily the least, nor the greatest one, whose existence is guaranteed by a smooth extension of classical results. This notion nicely subsumes standard inference systems and their inductive and coinductive interpretation, thus allowing formal reasoning in cases where the inductive and coinductive interpretation do not provide the intended meaning, but are rather mixed together. This is a corrected version of the paper (arXiv:1808.02943v4) published originally on 12 March 2019

    Volume: Volume 15, Issue 1
    Published on: February 20, 2020
    Accepted on: January 31, 2019
    Submitted on: August 10, 2018
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages,68Q55, 03B70,D.3.1,F.3.1,F.4.1

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