Apartness relations between propositions

• Published in: Mathematical logic quarterly Vol. 70; no. 4; pp. 414 - 428
• Main Author: Kocsis, Zoltan A.
• Format: Journal Article
• Language: English
• Published: Berlin Wiley Subscription Services, Inc 01.11.2024
• Subjects: Boolean algebra; Semantics

We classify all apartness relations definable in propositional logics extending intuitionistic logic using Heyting algebra semantics. We show that every Heyting algebra which contains a non‐trivial apartness term satisfies the weak law of excluded middle, and every Heyting algebra which contains a t...