Metodo

International Studies in Phenomenology and Philosophy

Book | Chapter

181257

The logic of the weak excluded middle

a case study of proof-search

Giovanna Corsi

pp. 95-116

Abstract

The logic J of the weak excluded middle, known also as Jankov's logic, is an extension of the intuitionistic logic obtained by adding the schema ¬A⋁¬¬A. This logic, we believe, offers a good case study for some metatheoretical properties: Is there a cut-free calculus for this logic? Is it analytic? Is there a proof-search procedure that answers the question whether a formula is a theorem or not, and if not, does it give us a strategy to build a countermodel? It is a well known result [4] that Lemma 1. (Hosoi) If a wff A contains the propositional letters p 1,...,p n then A is a theorem of J iff (¬p 1 ⋁ ¬¬p 1) ⋀ ⋯ ⋀ (¬p n ⋁ ¬¬p n ) → A is a theorem of the intuitionistic logic.

Publication details

Published in:

Lupacchini Rossella, Corsi Giovanna (2008) Deduction, computation, experiment: exploring the effectiveness of proof. Dordrecht, Springer.

Pages: 95-116

DOI: 10.1007/978-88-470-0784-0_6

Full citation:

Corsi Giovanna (2008) „The logic of the weak excluded middle: a case study of proof-search“, In: R. Lupacchini & G. Corsi (eds.), Deduction, computation, experiment, Dordrecht, Springer, 95–116.