Abstract
We are interested in frame definability of classes of trees, using formulas of the μ-calculus. In this set up, the proposition letters (or in other words, the free variables) in the μ-formulas correspond to second order variables over which universally quantify. Our main result is a semantic characterization of the MSO definable classes of trees that are definable by a μ-formula. We also show that it is decidable whether a given MSO formula corresponds to a μ-formula, in the sense that they define the same class of trees.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Goldblatt, R., Thomason, S.: Axiomatic classes in propositional modal logic. In: Algebra and Logic. Lecture Notes in Mathematics, vol. 450, pp. 163–173. Springer, Heidelberg (1975)
Janin, D., Lenzi, G.: On the relationship between moandic and weak monadic second order logic on arbitrary trees, with application to the mu-calculus. Fudamenta Informaticae 61, 247–265 (2003)
Janin, D., Walukiewicz, I.: Automata for the mu-calculus and related results. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969. Springer, Heidelberg (1995)
Janin, D., Walukiewicz, I.: On the expressive completeness of the propositional modal mu-calculus and related results. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119. Springer, Heidelberg (1996)
van Benthem, J.: Modal correspondance theory. PhD thesis, Mathematisch Instituut en Instituut voor Grondslagenonderzoek, University of Amsterdam (1976)
van Benthem, J.: Exploring logical dynamics. CSLI publications, Stanford (1996)
Walukiewicz, I.: Monadic second order logic on tree-like structures. Theoretical Computer Science 275, 311–346 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fontaine, G., Place, T. (2010). Frame Definability for Classes of Trees in the μ-calculus. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-15155-2_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15154-5
Online ISBN: 978-3-642-15155-2
eBook Packages: Computer ScienceComputer Science (R0)