Triple

T18793326
Position Surface form Disambiguated ID Type / Status
Subject Arend Heyting E459570 entity
Predicate notableFor P22 FINISHED
Object Heyting algebra
A Heyting algebra is a type of bounded lattice that models intuitionistic logic by providing an implication operation without requiring the law of excluded middle.
E1343171 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: Heyting algebra | Statement: [Arend Heyting, notableFor, Heyting algebra]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Heyting algebra
Context triple: [Arend Heyting, notableFor, Heyting algebra]
  • A. Brouwer–Heyting–Kolmogorov interpretation
    The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
  • B. Handbook of Boolean Algebras
    The *Handbook of Boolean Algebras* is a comprehensive multi-volume reference work that surveys the theory, structure, and applications of Boolean algebras in modern mathematics and logic.
  • C. Lattice Theory
    Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
  • D. Gödel–Löb provability logic (GL)
    Gödel–Löb provability logic (GL) is a modal logic system that formalizes reasoning about provability in arithmetic, capturing the behavior of the provability predicate in Peano Arithmetic.
  • E. Hilbert-style deductive systems
    Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel 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: Heyting algebra
Triple: [Arend Heyting, notableFor, Heyting algebra]
Generated description
A Heyting algebra is a type of bounded lattice that models intuitionistic logic by providing an implication operation without requiring the law of excluded middle.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Heyting algebra
Target entity description: A Heyting algebra is a type of bounded lattice that models intuitionistic logic by providing an implication operation without requiring the law of excluded middle.
  • A. Brouwer–Heyting–Kolmogorov interpretation
    The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
  • B. Handbook of Boolean Algebras
    The *Handbook of Boolean Algebras* is a comprehensive multi-volume reference work that surveys the theory, structure, and applications of Boolean algebras in modern mathematics and logic.
  • C. Lattice Theory
    Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
  • D. Gödel–Löb provability logic (GL)
    Gödel–Löb provability logic (GL) is a modal logic system that formalizes reasoning about provability in arithmetic, capturing the behavior of the provability predicate in Peano Arithmetic.
  • E. Hilbert-style deductive systems
    Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel 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_69d8d396f54c8190ba49db31e8743842 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e59787e5988190883ed575ab4b6dec completed April 20, 2026, 3:03 a.m.
NED1 Entity disambiguation (via context triple) batch_6a05472071b88190a74e18be8699f0c6 completed May 14, 2026, 3:53 a.m.
NEDg Description generation batch_6a054a44f0a8819089ebe23231d04ab8 completed May 14, 2026, 4:06 a.m.
NED2 Entity disambiguation (via description) batch_6a054ac3e8a88190981789df1790774e completed May 14, 2026, 4:08 a.m.
Created at: April 10, 2026, 11:53 a.m.