CTL and ECTL as fragments of the modal &mgr;-calculus
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
An introduction to distributed algorithms
An introduction to distributed algorithms
Modal logic
Distributed Algorithms
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
On the Expressive Power of CTL
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Modal logics for finite graphs
Logic for concurrency and synchronisation
Graph Theory With Applications
Graph Theory With Applications
A Logical Approach to Hamiltonian Graphs
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 0.00 |
Graphs are among the most frequently used structures in Computer Science. In this work, we analyze how we can express some important graph properties such as connectivity, acyclicity and the Eulerian and Hamiltonian properties in a modal logic. First, we show that these graph properties are not definable in a basic modal language. Second, we discuss an extension of the basic modal language with fix-point operators, the modal @m-calculus. Unfortunately, even with all its expressive power, the @m-calculus fails to express these properties. This happens because @m-calculus formulas are invariant under bisimulations. Third, we show that it is possible to express some of the above properties in a basic hybrid logic. Fourth, we propose an extension of CTL* with nominals, that we call hybrid-CTL*, and then show that it can express the Hamiltonian property in a better way than the basic hybrid logic. Finally, we introduce a promising way of expressing properties related to edges and use it to express the Eulerian property.