Triple
T14265203
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Peano arithmetic |
E353625
|
entity |
| Predicate | hasVariant |
P455
|
FINISHED |
| Object | first-order 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: first-order Peano arithmetic | Statement: [Peano arithmetic, hasVariant, first-order Peano arithmetic]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: first-order Peano arithmetic Context triple: [Peano arithmetic, hasVariant, first-order 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.
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.
-
C.
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.
-
D.
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.
-
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_69d8278c43e08190824146f4632b89a5 |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de6357a8188190ba518a486521052b |
completed | April 14, 2026, 3:55 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd326367348190b4b31b32f4ca5639 |
completed | May 8, 2026, 12:46 a.m. |
Created at: April 10, 2026, 1:09 a.m.