Triple

T14265518
Position Surface form Disambiguated ID Type / Status
Subject J. Donald Monk E353632 entity
Predicate hasWritten P2831 FINISHED
Object Introduction to Set Theory
Introduction to Set Theory is a foundational mathematics textbook that presents the basic concepts, methods, and results of modern set theory for advanced undergraduates and beginning graduate students.
E1090246 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: Introduction to Set Theory | Statement: [J. Donald Monk, hasWritten, Introduction to Set Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Introduction to Set Theory
Context triple: [J. Donald Monk, hasWritten, Introduction to Set Theory]
  • A. Einleitung in die Mengenlehre
    Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
  • B. Grundzüge der Mengenlehre
    Grundzüge der Mengenlehre is a foundational early 20th-century textbook on set theory that helped formalize and shape modern axiomatic set theory and topology.
  • C. set theory
    Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
  • D. Logic, Computers, and Sets
    Logic, Computers, and Sets is a foundational work by logician Hao Wang that explores the interconnections between mathematical logic, set theory, and the theory of computation.
  • E. Foundations of Set Theory (with Andrey Kolmogorov)
    "Foundations of Set Theory" is a classic 20th-century mathematical text co-authored by Pavel Alexandrov and Andrey Kolmogorov that systematically develops the basic concepts and axioms of set theory.
  • 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: Introduction to Set Theory
Triple: [J. Donald Monk, hasWritten, Introduction to Set Theory]
Generated description
Introduction to Set Theory is a foundational mathematics textbook that presents the basic concepts, methods, and results of modern set theory for advanced undergraduates and beginning graduate students.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Introduction to Set Theory
Target entity description: Introduction to Set Theory is a foundational mathematics textbook that presents the basic concepts, methods, and results of modern set theory for advanced undergraduates and beginning graduate students.
  • A. Einleitung in die Mengenlehre
    Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
  • B. Grundzüge der Mengenlehre
    Grundzüge der Mengenlehre is a foundational early 20th-century textbook on set theory that helped formalize and shape modern axiomatic set theory and topology.
  • C. set theory
    Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
  • D. Logic, Computers, and Sets
    Logic, Computers, and Sets is a foundational work by logician Hao Wang that explores the interconnections between mathematical logic, set theory, and the theory of computation.
  • E. Foundations of Set Theory (with Andrey Kolmogorov)
    "Foundations of Set Theory" is a classic 20th-century mathematical text co-authored by Pavel Alexandrov and Andrey Kolmogorov that systematically develops the basic concepts and axioms of set theory.
  • 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_69fd326551b08190ae8fe220a6422339 completed May 8, 2026, 12:46 a.m.
NEDg Description generation batch_69fd3417e8e88190b099bfe4ba30f364 completed May 8, 2026, 12:53 a.m.
NED2 Entity disambiguation (via description) batch_69fd37df3dfc8190a594abb2c14e11bb completed May 8, 2026, 1:09 a.m.
Created at: April 10, 2026, 1:09 a.m.