Triple

T17230037
Position Surface form Disambiguated ID Type / Status
Subject Hilbert-style deductive systems E418216 entity
Predicate appliesTo P1129 FINISHED
Object Peano arithmetic E353625 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: Peano arithmetic | Statement: [Hilbert-style deductive systems, appliesTo, Peano arithmetic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Peano arithmetic
Context triple: [Hilbert-style deductive systems, appliesTo, Peano arithmetic]
  • A. Peano arithmetic chosen
    Peano arithmetic is a formal first-order axiomatic system that captures the basic properties of the natural numbers and underpins much of modern mathematical logic and number theory.
  • B. Robinson arithmetic
    Robinson arithmetic is a weak formal system of arithmetic that captures basic properties of the natural numbers but is strictly weaker and less expressive than full Peano arithmetic.
  • C. Skolem arithmetic
    Skolem arithmetic is a fragment of first-order arithmetic focusing on the natural numbers with multiplication but without addition, studied for its distinctive decidability and model-theoretic properties.
  • D. Gödel numbering
    Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
  • E. Lectures on the Logic of Arithmetic
    Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
  • 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_69d886d8e96081909870bff6c3d0bf09 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e42df62ec48190b2ed633a5bcc0255 completed April 19, 2026, 1:20 a.m.
NED1 Entity disambiguation (via context triple) batch_6a01675eae08819093427b4dc1ffee5f completed May 11, 2026, 5:21 a.m.
Created at: April 10, 2026, 5:39 a.m.