Studia Logica 40 (2):113 - 139 (1981)
|Abstract||This paper studies, by way of an example, the intuitionistic propositional connective * defined in the language of second order propositional logic by. In full topological models * is not generally definable, but over Cantor-space and the reals it can be classically shown that; on the other hand, this is false constructively, i.e. a contradiction with Church's thesis is obtained. This is comparable with some well-known results on the completeness of intuitionistic first-order predicate logic.Over [0, 1], the operator * is (constructively and classically) undefinable. We show how to recast this argument in terms of intuitive intuitionistic validity in some parameter. The undefinability argument essentially uses the connectedness of [0, 1]; most of the work of recasting consists in the choice of a suitable intuitionistically meaningful parameter, so as to imitate the effect of connectedness.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Giambattista Amati, Luigia Carlucci-Aiello & Fiora Pirri (1997). Intuitionistic Autoepistemic Logic. Studia Logica 59 (1):103-120.
Morten H. Sørensen & Paweł Urzyczyn (2010). A Syntactic Embedding of Predicate Logic Into Second-Order Propositional Logic. Notre Dame Journal of Formal Logic 51 (4):457-473.
Philip Kremer (1997). On the Complexity of Propositional Quantification in Intuitionistic Logic. Journal of Symbolic Logic 62 (2):529-544.
Stefano Berardi (1999). Intuitionistic Completeness for First Order Classical Logic. Journal of Symbolic Logic 64 (1):304-312.
Tomasz Połacik (1998). Propositional Quantification in the Monadic Fragment of Intuitionistic Logic. Journal of Symbolic Logic 63 (1):269-300.
Milan Božić & Kosta Došen (1984). Models for Normal Intuitionistic Modal Logics. Studia Logica 43 (3):217 - 245.
Mitsuhiro Okada (1987). A Weak Intuitionistic Propositional Logic with Purely Constructive Implication. Studia Logica 46 (4):371 - 382.
Richard Zach (2004). Decidability of Quantified Propositional Intuitionistic Logic and S4 on Trees of Height and Arity ≤Ω. Journal of Philosophical Logic 33 (2):155-164.
Peter W. O'Hearn & David J. Pym (1999). The Logic of Bunched Implications. Bulletin of Symbolic Logic 5 (2):215-244.
Tomasz Połacik (1994). Second Order Propositional Operators Over Cantor Space. Studia Logica 53 (1):93 - 105.
Added to index2009-01-28
Total downloads8 ( #131,711 of 722,873 )
Recent downloads (6 months)1 ( #60,917 of 722,873 )
How can I increase my downloads?