Triple
T6594126
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stephen Kleene |
E148433
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Kleene’s normal form theorem
Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
|
E601580
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Kleene’s normal form theorem | Statement: [Stephen Kleene, knownFor, Kleene’s normal form theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kleene’s normal form theorem Context triple: [Stephen Kleene, knownFor, Kleene’s normal form theorem]
-
A.
Kleene numbering
Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
-
B.
arithmetization of syntax
Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
-
C.
Computability and Unsolvability
Computability and Unsolvability is a classic 1958 textbook by Martin Davis that systematically develops the theory of computable functions and undecidable problems, helping to shape modern computability theory.
-
D.
Tarski–Mostowski–Robinson theorem
The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
-
E.
Rice's theorem
Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Kleene’s normal form theorem Triple: [Stephen Kleene, knownFor, Kleene’s normal form theorem]
Generated description
Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kleene’s normal form theorem Target entity description: Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
-
A.
Kleene numbering
Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
-
B.
arithmetization of syntax
Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
-
C.
Computability and Unsolvability
Computability and Unsolvability is a classic 1958 textbook by Martin Davis that systematically develops the theory of computable functions and undecidable problems, helping to shape modern computability theory.
-
D.
Tarski–Mostowski–Robinson theorem
The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
-
E.
Rice's theorem
Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69c687e7b8688190811ffee72e096468 |
completed | March 27, 2026, 1:36 p.m. |
| NER | Named-entity recognition | batch_69c6aed0b364819081cb02af7a38ef11 |
completed | March 27, 2026, 4:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c6cbba656c81909c3876a8f2f7300e |
completed | March 27, 2026, 6:26 p.m. |
| NEDg | Description generation | batch_69c6cd09753c81909df166156ffbf82a |
completed | March 27, 2026, 6:31 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c6ce9ba47c819091496c87117e7a03 |
completed | March 27, 2026, 6:38 p.m. |
Created at: March 27, 2026, 1:55 p.m.