On the semantics of classical disjunction

✍ Scribed by David Pym; Eike Ritter

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 214 KB
• Volume: 159
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00161-4

✦ Synopsis

The -calculus provides a system of realizers for classical free (cf. natural) deduction in the absence of disjunction. We identify two forms of disjunction, one derived from Gentzen's sequent calculus LJ and one from LK, and develop the corresponding metatheory for extended with disjunction. We describe a class of categorical models for the -calculus with each of these disjunctions. Considering the calculus with LK-derived disjunction, , we establish the standard metatheoretic properties and show that a class of continuations models of can be elegantly extended to . Comparing the two forms of disjunction, we show that any model which identiÿes them collapses to a trivial family of Boolean algebras.