Kleene strong three-valued logic

E353399

logical system many-valued logic non-classical logic paracomplete logic paraconsistent logic three-valued logic

Kleene strong three-valued logic is a non-classical logical system that extends classical logic with a third truth value to rigorously handle indeterminate or partially defined statements.

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All labels observed (5)

Label	Occurrences
Kleene’s strong three-valued logic	2
Kleene strong three-valued logic canonical	1
Kleene’s strong logic of indeterminacy	1
Kleene’s weak three-valued logic	1
Three-Valued Logic	1

How this entity was disambiguated

This entity first appeared as the object of triple T3390236 — 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: Kleene strong three-valued logic
Context triple: [Kripke fixed-point theory of truth, oftenFormalizedWith, Kleene strong three-valued logic]

A. The Logic of Computer Programming
The Logic of Computer Programming is a foundational textbook in theoretical computer science that rigorously develops methods for specifying, proving, and reasoning about the correctness of computer programs.
B. 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.
C. Logical Methods in Computer Science
Logical Methods in Computer Science is a peer-reviewed open-access journal focusing on theoretical computer science, particularly logic and its applications to computer science.
D. Semantical Considerations on Modal Logic
Semantical Considerations on Modal Logic is a landmark philosophical paper by Saul Kripke that helped found possible-worlds semantics and revolutionized the study of modal logic.
E. Introduction to Logical Theory
Introduction to Logical Theory is a mid-20th-century philosophical work by P. F. Strawson that critically examines traditional formal logic and its relation to ordinary language.
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: Kleene strong three-valued logic
Target entity description: Kleene strong three-valued logic is a non-classical logical system that extends classical logic with a third truth value to rigorously handle indeterminate or partially defined statements.

A. The Logic of Computer Programming
The Logic of Computer Programming is a foundational textbook in theoretical computer science that rigorously develops methods for specifying, proving, and reasoning about the correctness of computer programs.
B. 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.
C. Logical Methods in Computer Science
Logical Methods in Computer Science is a peer-reviewed open-access journal focusing on theoretical computer science, particularly logic and its applications to computer science.
D. Semantical Considerations on Modal Logic
Semantical Considerations on Modal Logic is a landmark philosophical paper by Saul Kripke that helped found possible-worlds semantics and revolutionized the study of modal logic.
E. Introduction to Logical Theory
Introduction to Logical Theory is a mid-20th-century philosophical work by P. F. Strawson that critically examines traditional formal logic and its relation to ordinary language.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	logical system ⓘ many-valued logic ⓘ non-classical logic ⓘ paracomplete logic ⓘ paraconsistent logic ⓘ three-valued logic ⓘ
allowsTruthValue	both operands undefined in conjunction yield undefined ⓘ both operands undefined in disjunction yield undefined ⓘ
alsoKnownAs	K3 ⓘ Kleene’s strong logic of indeterminacy ⓘ linked to: Kleene strong three-valued logic
coincidesWithClassicalLogicOn	formulas without undefined values ⓘ
contradictionsAreExplosive	no ⓘ
designatedValuesInclude	true ⓘ
designatedValuesMayExclude	undefined ⓘ
extends	classical propositional logic ⓘ
hasApplicationDomain	computer science ⓘ mathematical logic ⓘ philosophical logic ⓘ
hasDesignGoal	to handle indeterminate statements ⓘ to model partial functions ⓘ to model partially defined predicates ⓘ
hasProperty	fails law of excluded middle in general ⓘ fails law of non-contradiction in general ⓘ non-bivalent semantics ⓘ truth-functional connectives ⓘ
hasSemanticFramework	three-valued matrices ⓘ
hasTruthValue	false ⓘ indeterminate ⓘ true ⓘ undefined ⓘ
introducedBy	Stephen Cole Kleene ⓘ linked to: Stephen Kleene
introducedFor	formalizing reasoning with partial functions ⓘ
namedAfter	Stephen Cole Kleene ⓘ linked to: Stephen Kleene
preservesClassicalValues	yes ⓘ
relatedLogic	Bochvar three-valued logic ⓘ Priest’s Logic of Paradox ⓘ linked to: An Introduction to Non-Classical Logic
supportsPartialValuations	yes ⓘ
treatmentOfTautologies	classical tautologies may fail to be designated ⓘ
truthFunctionOfConjunction	is truth-functional and three-valued ⓘ
truthFunctionOfDisjunction	is truth-functional and three-valued ⓘ
truthFunctionOfImplication	is truth-functional and three-valued ⓘ
truthFunctionOfNegation	maps false to true ⓘ maps true to false ⓘ maps undefined to undefined ⓘ
usedIn	formal semantics of programming languages ⓘ reasoning about partiality ⓘ reasoning about undefined terms ⓘ theory of partial recursive functions ⓘ

How these facts were elicited