The Unique Intermediate Logic Whose Every Rule is Archetypal
Tomasz Połacik · Logic Journal of IGPL · 2005
Informally, we can say that an inference rule is archetypal if any other rule can be transformed to it (up to suitable equivalence) via some substitution for the propositional variables. It was shown by L. Humberstone that, in the case of classical propositional logic, every non-degenerate binary rule is archetypal and conjectured that this result holds also for all rules in the full language. In this paper we provide a proof of this conjecture and show that it is the unique intermediate logic with this property.