Triple

T4492884
Position Surface form Disambiguated ID Type / Status
Subject completeness theorem for first-order logic E100620 entity
Predicate contrastsWith P278 FINISHED
Object incompleteness theorems E71396 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: incompleteness theorems | Statement: [completeness theorem for first-order logic, contrastsWith, incompleteness theorems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: incompleteness theorems
Context triple: [completeness theorem for first-order logic, contrastsWith, incompleteness theorems]
  • A. Gödel's incompleteness theorems chosen
    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.
  • B. 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.
  • C. Löb's theorem
    Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
  • D. Hilbert’s program
    Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
  • E. completeness theorem for first-order logic
    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.
  • 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.