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.