Triple
T17871996
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Löwenheim–Skolem theorem |
E446857
|
entity |
| Predicate | involves |
P1256
|
FINISHED |
| Object | Skolem functions |
—
|
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: Skolem functions | Statement: [Löwenheim–Skolem theorem, involves, Skolem functions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Skolem functions Context triple: [Löwenheim–Skolem theorem, involves, Skolem functions]
-
A.
Skolemization
chosen
Skolemization is a logical transformation technique that eliminates existential quantifiers by introducing Skolem functions or constants, commonly used in automated theorem proving and first-order logic.
-
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.
Herbrand function
The Herbrand function is a numerical tool in local class field theory that measures the ramification filtration of Galois groups, playing a key role in understanding how ramification behaves in extensions of local fields.
-
D.
Herbrand's theorem
Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
-
E.
Herbrand semantics
Herbrand semantics is a formal framework in logic and automated theorem proving that interprets first-order formulas over the Herbrand universe of ground terms to define truth and satisfiability.
- 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_69d8b9f4c22c819093c2680434472894 |
completed | April 10, 2026, 8:51 a.m. |
| NER | Named-entity recognition | batch_69e49aa30ff8819090c51c1d7767e952 |
completed | April 19, 2026, 9:04 a.m. |
Created at: April 10, 2026, 10:18 a.m.