David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 76 (3):307 - 328 (2004)
For the given logical calculus we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit exists it is represented by a real number between 0 and 1 which we may call the density of truth for the investigated logic. In this paper we apply this approach to the intuitionistic logic of one variable with implication and negation. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of one variable (see ). Actually, this paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part (more than 93%) of classical prepositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Hervé Fournier, Danièle Gardy, Antoine Genitrini & Marek Zaionc (2010). Tautologies Over Implication with Negative Literals. Mathematical Logic Quarterly 56 (4):388-396.
Similar books and articles
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Greg Restall (1997). Combining Possibilities and Negations. Studia Logica 59 (1):121-141.
Zofia Kostrzycka (2007). The Density of Truth in Monadic Fragments of Some Intermediate Logics. Journal of Logic, Language and Information 16 (3):283-302.
Dimiter Vakarelov (1985). An Application of Rieger-Nishimura Formulas to the Intuitionistic Modal Logics. Studia Logica 44 (1):79 - 85.
Ken-etsu Fujita (1998). On Proof Terms and Embeddings of Classical Substructural Logics. Studia Logica 61 (2):199-221.
Zofia Kostrzycka & Marek Zaionc (2008). Asymptotic Densities in Logic and Type Theory. Studia Logica 88 (3):385 - 403.
Lloyd Humberstone (2000). Contra-Classical Logics. Australasian Journal of Philosophy 78 (4):438 – 474.
Guram Bezhanishvili (2001). Glivenko Type Theorems for Intuitionistic Modal Logics. Studia Logica 67 (1):89-109.
Xavier Caicedo & Roberto Cignoli (2001). An Algebraic Approach to Intuitionistic Connectives. Journal of Symbolic Logic 66 (4):1620-1636.
Added to index2009-01-28
Total downloads13 ( #141,074 of 1,692,471 )
Recent downloads (6 months)2 ( #111,548 of 1,692,471 )
How can I increase my downloads?