Non-well-founded Deduction for Induction and Coinduction.

Research output: Contribution to conferencePaperpeer-review

Abstract

Induction and coinduction are both used extensively within
mathematics and computer science. Algebraic formulations of these principles make the duality between them apparent, but do not account well for the way they are commonly used in deduction. Generally, the formalization of these reasoning methods employs inference rules that express a general explicit (co)induction scheme. Non-well-founded proof theory provides an alternative, more robust approach for formalizing implicit (co)inductive reasoning. This approach has been extremely successful in recent years in supporting implicit inductive reasoning, but is not as well-developed in the context of coinductive reasoning. This paper reviews the general method of non-well-founded proofs, and puts forward a concrete natural framework for (co)inductive reasoning, based on (co)closure operators, that offers a concise framework in which inductive and coinductive reasoning are captured as we intuitively understand and use them. Through this framework we demonstrate the enormous potential of non-well-founded deduction, both in the foundational theoretical exploration of (co)inductive reasoning and in the provision of proof support for (co)inductive reasoning within (semi-)automated proof tools.
Original languageEnglish
Pages3-24
Number of pages22
DOIs
StatePublished - 2021
Event28th International Conference on Automated Deduction

Proceedings: Virtual Event
-
Duration: 12 Jul 202115 Jul 2021

Conference

Conference28th International Conference on Automated Deduction

Proceedings
Period12/07/2115/07/21

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