Skip Navigation



Journal of Logic and Computation Advance Access published online on June 26, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp034
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kostrzycka, Z.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

On the Density of Truth of Locally Finite Logics

Zofia Kostrzycka

Department of Mathematics and Applied Computer Science, University of Technology, Luboszycka 3, 45-036 Opole, Poland.
E-mail: z.kostrzycka{at}po.opole.pl

Received 1 September 2008.

We prove that the density of truth exists for a large class of locally finite (locally tabular) propositional logics. We are primarily interested in classical and intuitionistic logic and show that their implicational fragments have the same density. There are also given some locally finite logics without the density of truth.

Keywords: Density of truth; locally finite logics; the Lindenbaum algebras; intuitionistic logic; the Drmota–Lalley–Woods theorem



References

  1. Chagrow A, Zakharyaschev M. Modal Logic (1997) 35. Oxford Logic Guides.
  2. Chauvin B, Flajolet P, Gardy D, Gittenberger B. And/Or trees revisited. Combinatorics, Probability and Computing (2004) 13:475–497.[CrossRef]
  3. Flajolet P, Sedgewick R. Analitic combinatorics: functional equations, rational and algebraic functions. INRIA, Number 4103 (2001).
  4. Flajolet P, Odlyzko AM. Singularity analysis of generating functions. SIAM Journal on Discrete Mathematics (1990) 3:216–240.[CrossRef][Web of Science]
  5. Fournier H, Gardy D, Genitrini A, Zaionc M. Classical and intuitionistic logic are asymptotically identical. 177–193. Vol. 4646 of Lecture Notes in Computer Science.
  6. Gardy D, Woods AR. And/or tree probabilities of Boolean functions. Discrete Mathematics and Theoretical Computer Science (2005) 139–146.
  7. Jankov VA. Conjunctively indecomposable formulas in propositional calculi. Izv, Akad. Nauk USSSR Ser. Mat (1969) 33:18–38.
  8. Kostrzycka Z. On asymptotic divergency in equivalential logics. Mathematical Structures in Computer Science (2008) 18:1–14.[Web of Science]
  9. Kostrzycka Z. On the density of truth in modal logics. Discrete Mathematics and Theoretical Computer Science (2006) 161–170.
  10. Kostrzycka Z. On the density of implicational parts of intuitionistic and classical logics. Journal of Applied Non-Classical Logics (2003) 13:295–325.
  11. Kostrzycka Z. On density of truth of the intuitionistic logic in one variable. Discrete Mathematics and Theoretical Computer Science (2008) 453–464.
  12. Kostrzycka Z, Zaionc M. Statistics of intuitionistic versus classical logics. Studia Logica (2004) 76:307–328.[CrossRef]
  13. Kostrzycka Z, Zaionc M. Asymptotic densities in logic and type theory. Studia Logica (2008) 88:385–403.[CrossRef]
  14. Lefmann H, Savicky P. Some typical properties of large and/or boolean formulas. Random Structures and Algorithms (1997) 10:337–351.[CrossRef]
  15. Matecki G. Asymptotic density for equivalence. Electronic Notes in Theoretical Computer Science URL (2005) 140:81–91.[CrossRef]
  16. Moczurad M, Tyszkiewicz J, Zaionc M. Statistical properties of simple types. Mathematical Structures in Computer Science (2000) 10:575–594.[CrossRef]
  17. Statman R. On the existence of closed terms in the typed {lambda}-calculus, In. In: Combinatory Logics, Lambda Calculus and Formalism—Hindley JR, Seldin J, eds. (1980) Academic Press.
  18. Wilf HS. Generating functionology (1994) 2nd edn. Academic Press.
  19. Woods AR. Coloring Rules for Finite Trees, and Probabilities of Monadic Second Order Sentences. Random Structures Algorithms (1997) 10:453–485.[CrossRef][Web of Science]

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kostrzycka, Z.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?