Structural Completeness in bi-IPC
Rodrigo Nicolau Almeida, Nick Bezhanishvili
TL;DR
This paper investigates the structural completeness of bi-intuitionistic logic extensions, demonstrating that only classical logic achieves this property, with proofs provided for certain systems.
Contribution
It establishes that no bi-IPC extension other than classical logic is structurally complete, providing direct proofs for some systems.
Findings
Classical logic is uniquely structurally complete among bi-IPC extensions.
Most bi-IPC extensions are not passively structurally complete.
Active structural completeness is proven for specific simple systems.
Abstract
In this note we show that no extension of bi-intuitionistic logic, except for classical logic, is structurally complete; indeed, none of them are passively structurally complete. A direct proof of active structural completeness is given for some simple systems.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Logic, programming, and type systems