Triple

T14265196
Position Surface form Disambiguated ID Type / Status
Subject Peano arithmetic E353625 entity
Predicate isStrongerThan P2373 FINISHED
Object 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.
E1090019 NE FINISHED

How this triple was built (4 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: Robinson arithmetic | Statement: [Peano arithmetic, isStrongerThan, Robinson arithmetic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Robinson arithmetic
Context triple: [Peano arithmetic, isStrongerThan, Robinson arithmetic]
  • A. Peano arithmetic
    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. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • E. arithmetization of syntax
    Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Robinson arithmetic
Triple: [Peano arithmetic, isStrongerThan, Robinson arithmetic]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Robinson arithmetic
Target entity description: 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.
  • A. Peano arithmetic
    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. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • E. arithmetization of syntax
    Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
  • F. None of above. chosen

Provenance (5 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.
NEDg Description generation batch_69fd335a496881908689b5769bb677ae completed May 8, 2026, 12:50 a.m.
NED2 Entity disambiguation (via description) batch_69fd3445422c8190a22eaa4bef5fdf76 completed May 8, 2026, 12:54 a.m.
Created at: April 10, 2026, 1:09 a.m.