Asymptotic Properties of Logics
@article{Zaionc2003AsymptoticPO, title={Asymptotic Properties of Logics}, author={Marek Zaionc}, journal={Schedae Informaticae}, year={2003}, volume={12}, pages={129-138} }
This paper presents the number of results concerning problems of asymptotic densities in the variety of propositional logics. We investigate, for propositional formulas, the proportion of tautologies of the given length n against the number of all formulas of length n. We are specially interested in asymptotic behavior of this fraction. We show what the relation between a number of premises of an implicational formula and asymptotic probability of finding a formula with this number of premises…
No Paper Link Available
References
SHOWING 1-8 OF 8 REFERENCES
On the Asymptotic Density of Tautologies in Logic of Implication and Negation
- PhilosophyReports Math. Log.
- 2005
The paper solves the problem of finding the asymptotic probability of the set of tautologies of classical logic with one propositional variable, implication and negation and proves the existence of this limit for classical (and at the same time intuitionistic) logic of implication built with exactly one variable.
Statistical properties of simple types
- MathematicsMathematical Structures in Computer Science
- 2000
From the lower and upper bounds presented, it is deduced that at least 1/3 of classical tautologies are intuitionistic, or the density or asymptotic probability of provable intuitionistic propositional formulas in the set of all formulas.
Advanced Combinatorics: The Art of Finite and Infinite Expansions
- Mathematics
- 1974
I. Vocabulary of Combinatorial Analysis.- 1.1. Subsets of a Set Operations.- 1.2. Product Sets.- 1.3. Maps.- 1.4. Arrangements, Permutations.- 1.5. Combinations (without repetitions) or Blocks.- 1.6.…
Statistics of implicational logic, to appear in
- Electronic Notes in Theoretical Computer Science
Statistics of Intuitionistic versus Classical Logics
- PhilosophyStud Logica
- 2004
This paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part of classical prepositional calculus and may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.
Generatingfunctionology, Second edition
- 1994
Received November
- Received November
- 2002