Triple

T14256349
Position Surface form Disambiguated ID Type / Status
Subject Löb's theorem E353392 entity
Predicate relatedTo P37 FINISHED
Object Gödel's second incompleteness theorem 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: Gödel's second incompleteness theorem | Statement: [Löb's theorem, relatedTo, Gödel's second incompleteness theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gödel's second incompleteness theorem
Context triple: [Löb's theorem, relatedTo, Gödel's second incompleteness theorem]
  • 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. Rosser’s trick in incompleteness proofs
    Rosser’s trick in incompleteness proofs is a refinement of Gödel’s incompleteness argument that strengthens the result by avoiding the need for the assumption that the underlying formal system is ω-consistent.
  • E. Gentzen’s consistency proof for arithmetic
    Gentzen’s consistency proof for arithmetic is a landmark 1930s result in proof theory that established the consistency of Peano arithmetic using transfinite induction up to the ordinal ε₀.
  • 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_69d8278c43e08190824146f4632b89a5 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de62992a188190bc046fbab5a149d6 completed April 14, 2026, 3:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd4c2e7ee081909a70c9d9b32b6ce5 completed May 8, 2026, 2:36 a.m.
Created at: April 10, 2026, 1:09 a.m.