Triple
T4492889
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | completeness theorem for first-order logic |
E100620
|
entity |
| Predicate | laterProofMethod |
P7024
|
FINISHED |
| Object |
Henkin construction
Henkin construction is a model-building technique in first-order logic that extends a theory with new constants to ensure every consistent set of sentences has a model, thereby proving completeness.
|
E446858
|
NE FINISHED |
How this triple was built (5 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: Henkin construction | Statement: [completeness theorem for first-order logic, laterProofMethod, Henkin construction]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Henkin construction Context triple: [completeness theorem for first-order logic, laterProofMethod, Henkin construction]
-
A.
Fraenkel
Fraenkel is a surname most prominently associated with Abraham Fraenkel, a German-Israeli mathematician known for his foundational work in axiomatic set theory.
-
B.
Kehjistan
Kehjistan is a vast, ancient desert kingdom and major human civilization in the Diablo universe, known for its powerful mage clans, bustling trade cities, and deep ties to Sanctuary’s arcane history.
-
C.
Heno
Heno is a Welsh-language television magazine programme broadcast on S4C, featuring news, interviews, and cultural stories from across Wales.
-
D.
constructible universe
The constructible universe is a class model of set theory introduced by Kurt Gödel that systematically builds sets in hierarchical stages and shows the relative consistency of the axiom of choice and the generalized continuum hypothesis with ZF.
-
E.
Hausdorff
Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
- 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: Henkin construction Triple: [completeness theorem for first-order logic, laterProofMethod, Henkin construction]
Generated description
Henkin construction is a model-building technique in first-order logic that extends a theory with new constants to ensure every consistent set of sentences has a model, thereby proving completeness.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Henkin construction Target entity description: Henkin construction is a model-building technique in first-order logic that extends a theory with new constants to ensure every consistent set of sentences has a model, thereby proving completeness.
-
A.
Fraenkel
Fraenkel is a surname most prominently associated with Abraham Fraenkel, a German-Israeli mathematician known for his foundational work in axiomatic set theory.
-
B.
Kehjistan
Kehjistan is a vast, ancient desert kingdom and major human civilization in the Diablo universe, known for its powerful mage clans, bustling trade cities, and deep ties to Sanctuary’s arcane history.
-
C.
Heno
Heno is a Welsh-language television magazine programme broadcast on S4C, featuring news, interviews, and cultural stories from across Wales.
-
D.
constructible universe
The constructible universe is a class model of set theory introduced by Kurt Gödel that systematically builds sets in hierarchical stages and shows the relative consistency of the axiom of choice and the generalized continuum hypothesis with ZF.
-
E.
Hausdorff
Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
- F. None of above. chosen
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: laterProofMethod Context triple: [completeness theorem for first-order logic, laterProofMethod, Henkin construction]
-
A.
hasProofMethod
chosen
Indicates that there exists a specific method or technique used to establish or demonstrate the validity of something (such as a statement, claim, or theorem).
-
B.
requiresProofOf
Indicates that one entity must provide formal evidence or documentation to validate or authorize another entity.
-
C.
laterSignatory
Indicates that one party signed or agreed to something at a later time than another specified party.
-
D.
attestedBy
Indicates that the existence, occurrence, or validity of something is supported, confirmed, or documented by a specified source or authority.
-
E.
confirmationMethod
Indicates the means or process by which something is verified, validated, or confirmed as true or accepted.
- F. None of above.
Provenance (6 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_69bd43cdf15081909a4fa2585ff63b3e |
completed | March 20, 2026, 12:55 p.m. |
| NER | Named-entity recognition | batch_69bd5570ba0881908f5fb4f8d0730e64 |
completed | March 20, 2026, 2:10 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bd67b40fd4819098636b6f29304312 |
completed | March 20, 2026, 3:28 p.m. |
| NEDg | Description generation | batch_69bd688e84fc8190a8900be40e3cf694 |
completed | March 20, 2026, 3:32 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bd69bcf10c8190bd6ceb6bc604b3f5 |
completed | March 20, 2026, 3:37 p.m. |
| PD | Predicate disambiguation | batch_69bd5213e3d0819094b026989e686f01 |
completed | March 20, 2026, 1:56 p.m. |
Created at: March 20, 2026, 12:59 p.m.