Triple

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).

Phrase: Heyting implication | Statement: [Arend Heyting, hasConceptNamedAfter, Heyting implication]

Target entity: Heyting implication
Context triple: [Arend Heyting, hasConceptNamedAfter, Heyting implication]

• 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. Curry–Howard correspondence
  The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
• C. Hilbert–Bernays derivability conditions
  The Hilbert–Bernays derivability conditions are a set of formal requirements on provability predicates in arithmetic that underpin key results in mathematical logic, including Gödel’s incompleteness theorems and Löb’s theorem.
• 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. Proof Methods for Modal and Intuitionistic Logics
  "Proof Methods for Modal and Intuitionistic Logics" is a foundational textbook by logician Melvin Fitting that systematically develops semantic and proof-theoretic techniques for reasoning in modal and intuitionistic logic systems.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Heyting implication
Target entity description: Heyting implication is the intuitionistic logic counterpart of classical material implication, defined within Heyting algebras to capture constructive reasoning about "if–then" statements.

• 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. Curry–Howard correspondence
  The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
• C. Hilbert–Bernays derivability conditions
  The Hilbert–Bernays derivability conditions are a set of formal requirements on provability predicates in arithmetic that underpin key results in mathematical logic, including Gödel’s incompleteness theorems and Löb’s theorem.
• 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. Proof Methods for Modal and Intuitionistic Logics
  "Proof Methods for Modal and Intuitionistic Logics" is a foundational textbook by logician Melvin Fitting that systematically develops semantic and proof-theoretic techniques for reasoning in modal and intuitionistic logic systems.
• F. None of above. chosen