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.
Syntax
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
formula for all Act-derivatives, Φ must hold
formula for some Act-derivative, Φ must hold
Formal semantics
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 , , there is no state for which , 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 .
See also
The modal μ-calculus, which extends HML with fixed point operators
Dynamic logic, a multimodal logic with infinitely many modalities
References
Sources
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.
Concurrency (computer science) Formal specification Modal logic Logic in computer science