Triple

T4492870
Position Surface form Disambiguated ID Type / Status
Subject completeness theorem for first-order logic E100620 entity
Predicate alsoKnownAs P39 FINISHED
Object Gödel's completeness theorem E100620 NE FINISHED

How this triple was built (2 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: Gödel's completeness theorem | Statement: [completeness theorem for first-order logic, alsoKnownAs, Gödel's completeness theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gödel's completeness theorem
Context triple: [completeness theorem for first-order logic, alsoKnownAs, Gödel's completeness theorem]
  • A. completeness theorem for first-order logic chosen
    The completeness theorem for first-order logic is a fundamental result in mathematical logic, proved by Kurt Gödel, which states that every logically valid first-order formula is provable from the axioms of first-order logic.
  • B. 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.
  • C. Herbrand's theorem
    Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
  • D. Tarski's undefinability theorem
    Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
  • E. Gödel's incompleteness theorems
    Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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.
Created at: March 20, 2026, 12:59 p.m.