Triple

T18793224
Position Surface form Disambiguated ID Type / Status
Subject Brouwer–Heyting–Kolmogorov interpretation E459568 entity
Predicate field P3 FINISHED
Object proof theory — NE NERFINISHED

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: proof theory | Statement: [Brouwer–Heyting–Kolmogorov interpretation, field, proof theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: proof theory
Context triple: [Brouwer–Heyting–Kolmogorov interpretation, field, proof theory]
  • A. proof theory chosen
    Proof theory is a branch of mathematical logic that studies the structure, properties, and formalization of mathematical proofs using symbolic and syntactic methods.
  • B. Mathematical Logic
    Mathematical Logic is a branch of mathematics and logic that studies formal systems, proof theory, model theory, recursion theory, and set theory to rigorously analyze the foundations of mathematics and reasoning.
  • C. Gentzen-style proof systems
    Gentzen-style proof systems are formal logical calculi, such as natural deduction and sequent calculi, that rigorously structure proofs using inference rules to clarify the foundations of mathematics and logic.
  • D. Recherches sur la théorie de la démonstration
    Recherches sur la théorie de la démonstration is Jacques Herbrand’s foundational work in mathematical logic, introducing key results in proof theory and what is now known as Herbrand’s theorem.
  • 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 (2 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_69d8d396f54c8190ba49db31e8743842 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e59787e5988190883ed575ab4b6dec completed April 20, 2026, 3:03 a.m.
Created at: April 10, 2026, 11:53 a.m.