Kripke frame
E949472
A Kripke frame is a mathematical structure used in modal logic, consisting of a set of possible worlds together with a relation specifying which worlds are accessible from which others.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Kripke model | 2 |
| Kripke frame canonical | 1 |
| Kripke structures | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11850296 — 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: Kripke frame Context triple: [Semantical Considerations on Modal Logic, hasConcept, Kripke frame]
-
A.
Kripke fixed-point theory of truth
The Kripke fixed-point theory of truth is a semantic framework developed by Saul Kripke that uses partial truth predicates and fixed points to consistently handle self-referential sentences and semantic paradoxes like the liar paradox.
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B.
Kripke–Platek set theory
Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
-
C.
An Essay in Modal Logic
An Essay in Modal Logic is a foundational philosophical work by G. H. von Wright that systematically develops the principles and systems of modal logic.
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D.
Fitting semantics for modal logic
Fitting semantics for modal logic is a framework in mathematical logic that extends Kripke-style semantics to provide a more general and often intuitionistic treatment of modal operators.
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E.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
- 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: Kripke frame Target entity description: A Kripke frame is a mathematical structure used in modal logic, consisting of a set of possible worlds together with a relation specifying which worlds are accessible from which others.
-
A.
Kripke fixed-point theory of truth
The Kripke fixed-point theory of truth is a semantic framework developed by Saul Kripke that uses partial truth predicates and fixed points to consistently handle self-referential sentences and semantic paradoxes like the liar paradox.
-
B.
Kripke–Platek set theory
Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
-
C.
An Essay in Modal Logic
An Essay in Modal Logic is a foundational philosophical work by G. H. von Wright that systematically develops the principles and systems of modal logic.
-
D.
Fitting semantics for modal logic
Fitting semantics for modal logic is a framework in mathematical logic that extends Kripke-style semantics to provide a more general and often intuitionistic treatment of modal operators.
-
E.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical structure
ⓘ
semantic structure in modal logic ⓘ |
| appliedIn |
computer science
ⓘ
formal epistemology ⓘ program verification ⓘ |
| canHaveProperty |
Euclidean accessibility relation
ⓘ
reflexive accessibility relation ⓘ serial accessibility relation ⓘ symmetric accessibility relation ⓘ transitive accessibility relation ⓘ |
| correspondsTo |
normal modal logic systems via frame conditions
ⓘ
system S4 via reflexive and transitive frames ⓘ system S5 via equivalence relation frames ⓘ system T via reflexive frames ⓘ |
| distinguishedFrom | Kripke model which also includes a valuation function ⓘ |
| formalDefinition | pair (W,R) where W is a nonempty set and R is a binary relation on W ⓘ |
| generalizes | relational models for necessity and possibility ⓘ |
| hasAccessibilityRelationType | binary relation on W × W ⓘ |
| hasComponent |
accessibility relation
ⓘ
set of possible worlds ⓘ |
| hasComponentRole |
accessibility relation represents reachability between worlds
ⓘ
worlds represent possible states or situations ⓘ |
| hasConstraint | W is usually required to be nonempty ⓘ |
| hasDomain | set W of possible worlds ⓘ |
| hasNotation | (W,R) ⓘ |
| hasRelation | binary relation R on W ⓘ |
| introducedInField |
mathematical logic
ⓘ
philosophical logic ⓘ |
| namedAfter | Saul Kripke ⓘ |
| provides | relational semantics for modal logics ⓘ |
| relatedConcept |
Kripke model
ⓘ
linked to:
Kripke frame
Kripke semantics ⓘ |
| usedFor |
interpreting deontic operators
ⓘ
interpreting knowledge operators ⓘ interpreting modal operators ⓘ interpreting necessity ⓘ interpreting possibility ⓘ interpreting temporal operators ⓘ |
| usedIn |
deontic logic
ⓘ
dynamic logic ⓘ epistemic logic ⓘ intuitionistic logic ⓘ modal logic ⓘ temporal logic ⓘ |
| usedToDefine | truth of modal formulas at worlds ⓘ |
| usedToStudy |
bisimulation between models
ⓘ
completeness of modal logics ⓘ correspondence theory in modal logic ⓘ |
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: Kripke frame Description of subject: A Kripke frame is a mathematical structure used in modal logic, consisting of a set of possible worlds together with a relation specifying which worlds are accessible from which others.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Kripke frame
linked to: Kripke frame
linked to: Kripke frame