# Density of truth in modal logics

Abstract : The aim of this paper is counting the probability that a random modal formula is a tautology. We examine $\{ \to,\Box \}$ fragment of two modal logics $\mathbf{S5}$ and $\mathbf{S4}$ over the language with one propositional variable. Any modal formula written in such a language may be interpreted as a unary binary tree. As it is known, there are finitely many different formulas written in one variable in the logic $\mathbf{S5}$ and this is the key to count the proportion of tautologies of $\mathbf{S5}$ among all formulas. Although the logic $\mathbf{S4}$ does not have this property, there exist its normal extensions having finitely many non-equivalent formulas.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [17 references]

https://hal.inria.fr/hal-01184704
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 17, 2015 - 2:24:34 PM
Last modification on : Thursday, May 11, 2017 - 1:02:51 AM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:09:16 PM

### File

dmAG0109.pdf
Publisher files allowed on an open archive

### Citation

Zofia Kostrzycka. Density of truth in modal logics. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.161-170, ⟨10.46298/dmtcs.3500⟩. ⟨hal-01184704⟩

Record views