Triple
T14256368
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Löb's theorem |
E353392
|
entity |
| Predicate | holdsIn |
P17841
|
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: [Löb's theorem, holdsIn, Peano arithmetic]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Peano arithmetic Context triple: [Löb's theorem, holdsIn, 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.
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.
-
D.
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.
-
E.
Peano notation
Peano notation is a formal symbolic system for representing natural numbers and arithmetic operations using axioms and successor functions, developed by Giuseppe Peano.
- 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_69fd325f213881909acf776ff4831c30 |
completed | May 8, 2026, 12:46 a.m. |
Created at: April 10, 2026, 1:09 a.m.