Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-02-03T03:30:26.879Z Has data issue: false hasContentIssue false
  • English
  • Français

On asymptotic divergency in equivalential logics

Published online by Cambridge University Press:  01 April 2008

ZOFIA KOSTRZYCKA
ZOFIA KOSTRZYCKA*
Affiliation:
University of Technology, Luboszycka 3, 45-036 Opole, Poland Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we characterise the equivalential reducts of classical and intuitionistic logics over a language with two propositional variables. We then investigate the size of the fraction of the tautologies of these logics against all formulas. Some methods from complex analysis are used to achieve this goal.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Issue 2 , April 2008 , pp. 311 - 324
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Flajolet, P. and Odlyzko, A. S. (1990) Singularity analysis of generating functions. SIAM J. on Discrete Math. 3 (2)216–240.Google Scholar
Flajolet, P. and Sedgewick, R. (2001) Analytic combinatorics: functional equations, rational and algebraic functions. INRIA, Number 4103.Google Scholar
Kostrzycka, Z. (2003) On the density of implicational parts of intuitionistic and classical logics. Journal of Applied Non-Classical Logics 13 (3)295–325.Google Scholar
Kostrzycka, Z. and Zaionc, M. (2004) Statistics of intuitionistic versus classical logics. Studia Logica 76 307–328.CrossRefGoogle Scholar
Matecki, G. (2005) Asymptotic density for equivalence. Electronic Notes in Theoretical Computer Science 140 81–91.CrossRefGoogle Scholar
Moczurad, M., Tyszkiewicz, J. and Zaionc, M. (2000) Statistical properties of simple types. Mathematical Structures in Computer Science 10 575–594.CrossRefGoogle Scholar
Słomczyńska, K. (1996) Equivalential algebras. Part I: Representation. Algebra Universalis 35 524–547.CrossRefGoogle Scholar
Szegö, G. (1975) Orthogonal polynomials, Fourth edition, AMS Colloquium Publications 23.Google Scholar
Wilf, H. S. (1994) Generating functionology, Second edition, Academic Press.Google Scholar
Wroński, A. (1993) On the free equivalential algebras with three generators. Bulletin of the Section of Logic 22 37–39.Google Scholar
Zaionc, M. (2004) On the asymptotic density of tautologies in logic of implication and negation. Reports on Mathematical Logic 38.Google Scholar