Heyting implication
E1343173
UNEXPLORED
Heyting implication is the intuitionistic logic counterpart of classical material implication, defined within Heyting algebras to capture constructive reasoning about "if–then" statements.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Heyting implication canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T18793339 — 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: Heyting implication Context triple: [Arend Heyting, hasConceptNamedAfter, Heyting implication]
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A.
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.
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B.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
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C.
Hilbert–Bernays derivability conditions
The Hilbert–Bernays derivability conditions are a set of formal requirements on provability predicates in arithmetic that underpin key results in mathematical logic, including Gödel’s incompleteness theorems and Löb’s theorem.
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D.
Gödel–Löb provability logic (GL)
Gödel–Löb provability logic (GL) is a modal logic system that formalizes reasoning about provability in arithmetic, capturing the behavior of the provability predicate in Peano Arithmetic.
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E.
Proof Methods for Modal and Intuitionistic Logics
"Proof Methods for Modal and Intuitionistic Logics" is a foundational textbook by logician Melvin Fitting that systematically develops semantic and proof-theoretic techniques for reasoning in modal and intuitionistic logic systems.
- 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: Heyting implication Target entity description: Heyting implication is the intuitionistic logic counterpart of classical material implication, defined within Heyting algebras to capture constructive reasoning about "if–then" statements.
-
A.
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.
-
B.
Curry–Howard correspondence
The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
-
C.
Hilbert–Bernays derivability conditions
The Hilbert–Bernays derivability conditions are a set of formal requirements on provability predicates in arithmetic that underpin key results in mathematical logic, including Gödel’s incompleteness theorems and Löb’s theorem.
-
D.
Gödel–Löb provability logic (GL)
Gödel–Löb provability logic (GL) is a modal logic system that formalizes reasoning about provability in arithmetic, capturing the behavior of the provability predicate in Peano Arithmetic.
-
E.
Proof Methods for Modal and Intuitionistic Logics
"Proof Methods for Modal and Intuitionistic Logics" is a foundational textbook by logician Melvin Fitting that systematically develops semantic and proof-theoretic techniques for reasoning in modal and intuitionistic logic systems.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.