# 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 :
Type de document :
Communication dans un congrès
Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.161-170, 2006, DMTCS Proceedings
Domaine :

Littérature citée [17 références]

https://hal.inria.fr/hal-01184704
Contributeur : Coordination Episciences Iam <>
Soumis le : lundi 17 août 2015 - 14:24:34
Dernière modification le : jeudi 11 mai 2017 - 01:02:51
Document(s) archivé(s) le : mercredi 18 novembre 2015 - 12:09:16

### Fichier

dmAG0109.pdf
Fichiers éditeurs autorisés sur une archive ouverte

### Identifiants

• HAL Id : hal-01184704, version 1

### Citation

Zofia Kostrzycka. Density of truth in modal logics. Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.161-170, 2006, DMTCS Proceedings. 〈hal-01184704〉

### Métriques

Consultations de la notice

## 42

Téléchargements de fichiers