Name
Abstract | ||
|---|---|---|
For the given logical calculus we investigate the size of the proportion of the number of true formulas of a certain length n against the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to inflnity. If the limit of fractions exists it represents the 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 it to the same problem 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 then 93%) of classical propositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on under- standing how much the phenomenon of truth is sporadic or frequent in random mathematics sentences. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1023/B:STUD.0000032101.88511.93 | Studia Logica |
Keywords | Field | DocType |
prepositional logic,asymptotic density of tautologies,probabilistic methods in logic | Intuitionistic logic,Discrete mathematics,Computability logic,Negation,Paraconsistent logic,Truth value,Minimal logic,Algorithm,Many-valued logic,Intermediate logic,Mathematics | Journal |
Volume | Issue | ISSN |
76 | 3 | 1572-8730 |
Citations | PageRank | References |
17 | 1.35 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zofia Kostrzycka | 1 | 37 | 5.59 |
| Marek Zaionc | 2 | 111 | 17.27 |