In computer science

Computer science

Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

, Hennessy–Milner logic (HML) is a multimodal logic

Multimodal logic

A multimodal logic is a modal logic that has more than one primitive modal operator. They find substantial applications in theoretical computer science....

 used to specify properties of a labeled transition system, a structure similar to an automaton. It was introduced in 1980 by Matthew Hennessy

Matthew Hennessy

Matthew Hennessy is an Irish computer scientist who has contributed especially to concurrency , process calculi and programming language semantics....

 and Robin Milner

Robin Milner

Arthur John Robin Gorell Milner FRS FRSE was a prominent British computer scientist.-Life, education and career:...

 in their paper 'On observing nondeterminism and concurrency' (ICALP).

Syntax

A formula is defined by the following BNF grammar for L some set of actions:


That is, a formula can be

constant truth : always true
constant false : always false
formula conjunction

Logical conjunction

In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false....

formula disjunction

Logical disjunction

In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true. E.g. in this context, "A or B" is true if A is true, or if B is true, or if both A and B are...

formula : for all L-derivatives, Φ must hold
formula : for some L-derivative, Φ must hold

See also

• The modal μ-calculus extends HML with fixed point operators.
• Dynamic logic
  Dynamic logic (modal logic)
  Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs and later applied to more general complex behaviors arising in linguistics, philosophy, AI, and other fields.-Language:...
  
  , a multimodal logic with infinitely many modalities.