David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 88 (3):385 - 403 (2008)
This paper presents a systematic approach for obtaining results from the area of quantitative investigations in logic and type theory. We investigate the proportion between tautologies (inhabited types) of a given length n against the number of all formulas (types) of length n. We investigate an asymptotic behavior of this fraction. Furthermore, we characterize the relation between number of premises of implicational formula (type) and the asymptotic probability of finding such formula among the all ones. We also deal with a distribution of these asymptotic probabilities. Using the same approach we also prove that the probability that randomly chosen fourth order type (or type of the order not greater than 4), which admits decidable lambda definability problem, is zero.
|Keywords||Philosophy Computational Linguistics Mathematical Logic and Foundations Logic|
|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
No citations found.
Similar books and articles
James F. Lynch (1997). Infinitary Logics and Very Sparse Random Graphs. Journal of Symbolic Logic 62 (2):609-623.
Nicola Gambino & Peter Aczel (2006). The Generalised Type-Theoretic Interpretation of Constructive Set Theory. Journal of Symbolic Logic 71 (1):67 - 103.
Adam J. Grove, Joseph Y. Halpern & Daphne Koller (1996). Asymptotic Conditional Probabilities: The Non-Unary Case. Journal of Symbolic Logic 61 (1):250-276.
M. D. G. Swaen (1991). The Logic of First Order Intuitionistic Type Theory with Weak Sigma- Elimination. Journal of Symbolic Logic 56 (2):467-483.
Anne Vedø (1997). Asymptotic Probabilities for Second-Order Existential Kahr-Moore-Wang Sentences. Journal of Symbolic Logic 62 (1):304-319.
Zofia Kostrzycka & Marek Zaionc (2004). Statistics of Intuitionistic Versus Classical Logics. Studia Logica 76 (3):307 - 328.
Added to index2009-01-28
Total downloads13 ( #179,414 of 1,699,588 )
Recent downloads (6 months)6 ( #105,649 of 1,699,588 )
How can I increase my downloads?