On the Structure of Inductive Reasoning: Circular and Tree-Shaped Proofs in the µ-Calculus
نویسندگان
چکیده
In this paper we study induction in the context of the firstorder μ-calculus with explicit approximations. We present and compare two Gentzen-style proof systems each using a different type of induction. The first is based on finite proof trees and uses a local well-founded induction rule, while the second is based on (finitely represented) ω-regular proof trees and uses a global induction discharge condition to ensure externally that all inductive reasoning is well-founded. We give effective procedures for the translation of proofs between the two systems, thus establishing their equivalence.
منابع مشابه
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