Dagnino, Francesco - Coaxioms: flexible coinductive definitions by inference systems

lmcs:4745 - Logical Methods in Computer Science, March 12, 2019, Volume 15, Issue 1
Coaxioms: flexible coinductive definitions by inference systems

Authors: Dagnino, Francesco

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.

Source : oai:arXiv.org:1808.02943
DOI : 10.23638/LMCS-15(1:26)2019
Volume: Volume 15, Issue 1
Published on: March 12, 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