Interpolation theorems for intuitionistic predicate logic

✍ Scribed by G. Mints

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 137 KB
• Volume: 113
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(01)00060-4

✦ Synopsis

Craig interpolation theorem (which holds for intuitionistic logic) implies that the derivability of X; X ⇒ Y implies existence of an interpolant I in the common language of X and X ⇒ Y such that both X ⇒ I and I; X ⇒ Y are derivable. For classical logic this extends to X; X ⇒ Y; Y , but for intuitionistic logic there are counterexamples. We present a version true for intuitionistic propositional (but not for predicate) logic, and more complicated version for the predicate case.