Hennessy–Milner logic

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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"[1] (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'.[2] Recursion is enabled with the use of maximum and minimum fixed points.

Syntax

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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

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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

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References

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  1. ^ Hennessy, Matthew; Milner, Robin (1980-07-14). "On observing nondeterminism and concurrency". Automata, Languages and Programming. Lecture Notes in Computer Science. Vol. 85. Springer, Berlin, Heidelberg. pp. 299–309. doi:10.1007/3-540-10003-2_79. ISBN 978-3540100034.
  2. ^ Holmström, Sören (1990). "Hennessy-Milner Logic with recursion as a specification language, and a refinement calculus based on it". Specification and Verification of Concurrent Systems. Workshops in Computing. pp. 294–330. doi:10.1007/978-1-4471-3534-0_15. ISBN 978-3-540-19581-8.

Sources

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  • 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.