Zofia Kostrzycka
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Density of truth in modal logics
dmtcs:3500 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2006,
DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
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https://doi.org/10.46298/dmtcs.3500
Density of truth in modal logicsConference paper
Authors: Zofia Kostrzycka 1,2
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Zofia Kostrzycka
1 University of Technology
2 Opole University of Technology
The aim of this paper is counting the probability that a random modal formula is a tautology. We examine {→,◻} fragment of two modal logics S5 and 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 S5 and this is the key to count the proportion of tautologies of S5 among all formulas. Although the logic S4 does not have this property, there exist its normal extensions having finitely many non-equivalent formulas.
Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: density of truth,Grzegorczyk's logic,S5 modal logic,[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Bibliographic References
3 Documents citing this article
Hervé Fournier;Danièle Gardy;Antoine Genitrini;None Bernhard Gittenberger, 2011, The fraction of large random trees representing a given Boolean function in implicational logic, Random Structures and Algorithms, 40, 3, pp. 317-349, 10.1002/rsa.20379.
Hervé Fournier;Danièle Gardy;Antoine Genitrini;Bernhard Gittenberger, Lecture notes in computer science, Complexity and Limiting Ratio of Boolean Functions over Implication, pp. 347-362, 2008, 10.1007/978-3-540-85238-4_28.
Zofia Kostrzycka;Marek Zaionc, 2008, Asymptotic Densities in Logic and Type Theory, Studia Logica, 88, 3, pp. 385-403, 10.1007/s11225-008-9110-0.