In computer science, Hennessy–Milner logic (HML) is a dynamic logic used to specify properties of a labeled transition system (LTS), a structure similar to an automaton. It was introduced in 1980 by Matthew Hennessy and Robin Milner in their paper "On observing nondeterminism and concurrency" (ICALP).
Another variant of the HML involves the use of recursion to extend the expressibility of the logic, and is commonly referred to as 'Hennessy-Milner Logic with recursion'. Recursion is enabled with the use of maximum and minimum fixed points.
A formula is defined by the following BNF grammar for Act some set of actions:
That is, a formula can be
- constant truth
- always true
- constant false
- always false
- formula conjunction
- formula disjunction
- for all Act-derivatives, Φ must hold
- for some Act-derivative, Φ must hold
Let be a labeled transition system, and let be the set of HML formulae. The satisfiability relation relates states of the LTS to the formulae they satisfy, and is defined as the smallest relation such that, for all states and formulae ,
- if there exists a state such that and , then ,
- if for all such that it holds that , then ,
- if , then ,
- if , then ,
- if and , then .
- The modal μ-calculus, which extends HML with fixed point operators
- Dynamic logic, a multimodal logic with infinitely many modalities
- Hennessy, Matthew; Milner, Robin (1980-07-14). "On observing nondeterminism and concurrency". Automata, Languages and Programming. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg: 299–309. doi:10.1007/3-540-10003-2_79. ISBN 3540100032.
- Holmström, Sören (1990). "Hennessy-Milner Logic with Recursion as a Specification Language, and a Refinement Calculus based on It". Proceedings of the BCS-FACS Workshop on Specification and Verification of Concurrent Systems: 294–330.
- Colin P. Stirling (2001). Modal and temporal properties of processes. Springer. pp. 32–39. ISBN 978-0-387-98717-0.
- Sören Holmström. 1988. "Hennessy-Milner Logic with Recursion as a Specification Language, and a Refinement Calculus based on It". In Proceedings of the BCS-FACS Workshop on Specification and Verification of Concurrent Systems, Charles Rattray (Ed.). Springer-Verlag, London, UK, 294–330.
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