mu-calculus
E824073
The mu-calculus is a powerful modal logic with fixed-point operators used to express and verify properties of recursive and infinite-state systems in computer science.
All labels observed (3)
| Label | Occurrences |
|---|---|
| mu-calculus canonical | 2 |
| alternation-free μ-calculus | 1 |
| higher-order μ-calculus | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9838453 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: mu-calculus Context triple: [Dexter Kozen, knownFor, mu-calculus]
-
A.
branching-time temporal logic CTL*
Branching-time temporal logic CTL* is a highly expressive formalism in computer science used to specify and reason about the behavior of concurrent and reactive systems over branching time structures.
-
B.
linear temporal logic
Linear temporal logic is a modal temporal logic used in computer science and formal methods to specify and reason about the behavior of systems over linear sequences of time, using operators that describe how properties evolve in the future.
-
C.
Kleene algebra
Kleene algebra is an algebraic structure used to model and reason about regular expressions, program control flow, and formal languages through operations like choice, sequencing, and iteration.
-
D.
π-calculus
The π-calculus is a formal mathematical model for describing and analyzing concurrent, communicating systems, particularly those with dynamic network structures.
-
E.
Hoare logic
Hoare logic is a formal system in computer science used to reason rigorously about the correctness of computer programs using logical assertions about program states.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: mu-calculus Target entity description: The mu-calculus is a powerful modal logic with fixed-point operators used to express and verify properties of recursive and infinite-state systems in computer science.
-
A.
branching-time temporal logic CTL*
Branching-time temporal logic CTL* is a highly expressive formalism in computer science used to specify and reason about the behavior of concurrent and reactive systems over branching time structures.
-
B.
linear temporal logic
Linear temporal logic is a modal temporal logic used in computer science and formal methods to specify and reason about the behavior of systems over linear sequences of time, using operators that describe how properties evolve in the future.
-
C.
Kleene algebra
Kleene algebra is an algebraic structure used to model and reason about regular expressions, program control flow, and formal languages through operations like choice, sequencing, and iteration.
-
D.
π-calculus
The π-calculus is a formal mathematical model for describing and analyzing concurrent, communicating systems, particularly those with dynamic network structures.
-
E.
Hoare logic
Hoare logic is a formal system in computer science used to reason rigorously about the correctness of computer programs using logical assertions about program states.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
fixpoint logic
ⓘ
modal logic ⓘ temporal logic formalism ⓘ |
| canExpress |
fairness properties
ⓘ
liveness properties ⓘ reachability properties ⓘ safety properties ⓘ ω-regular properties ⓘ |
| complexityOfModelChecking | EXPTIME-complete for general formulas ⓘ |
| field |
mathematical logic
ⓘ
theoretical computer science ⓘ |
| hasDecisionProcedure |
automata-theoretic model checking
ⓘ
parity game solving ⓘ |
| hasFeature |
ability to express recursive properties
ⓘ
alternation of least and greatest fixpoints ⓘ fixed-point quantification over predicates ⓘ modal operators for necessity and possibility ⓘ |
| hasOperator |
greatest fixpoint operator ν
ⓘ
least fixpoint operator μ ⓘ |
| hasSyntaxBasedOn |
boolean connectives
ⓘ
fixpoint operators ⓘ modalities ⓘ propositional variables ⓘ |
| hasVariant |
alternation-free μ-calculus
ⓘ
linked to:
mu-calculus
higher-order μ-calculus ⓘ
linked to:
mu-calculus
probabilistic μ-calculus ⓘ |
| introducedInField | modal logic ⓘ |
| moreExpressiveThan |
CTL
ⓘ
linked to:
CTL*
CTL* ⓘ LTL ⓘ |
| relatedTo |
automata theory
ⓘ
game semantics ⓘ parity automata ⓘ |
| semanticsGivenBy |
Kripke structures
ⓘ
linked to:
Kripke semantics
transition systems ⓘ |
| semanticsUses |
least and greatest fixed points
ⓘ
monotone operators on power sets ⓘ |
| subsumes |
Computation Tree Logic
ⓘ
linked to:
branching-time temporal logic CTL*
Computation Tree Logic* ⓘ Linear Temporal Logic ⓘ
linked to:
linear temporal logic
many standard temporal logics ⓘ |
| typicalApplicationDomain |
verification of communication protocols
ⓘ
verification of concurrent systems ⓘ |
| usedFor |
expressing properties of infinite-state systems
ⓘ
expressing properties of recursive programs ⓘ model checking ⓘ specification of properties of transition systems ⓘ verification of reactive systems ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: mu-calculus Description of subject: The mu-calculus is a powerful modal logic with fixed-point operators used to express and verify properties of recursive and infinite-state systems in computer science.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Model Checking (book)
subject linked to:
mu-calculus
linked to: mu-calculus
subject linked to:
mu-calculus
linked to: mu-calculus