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: Brouwer–Heyting logic | Statement: [intuitionism, relatedTo, Brouwer–Heyting logic]

Target entity: Brouwer–Heyting logic
Context triple: [intuitionism, relatedTo, Brouwer–Heyting logic]

• 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. Heyting arithmetic
  Heyting arithmetic is a formal system of arithmetic based on intuitionistic logic, serving as the constructive counterpart to classical Peano arithmetic.
• C. 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.
• D. 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.
• E. Heyting implication
  Heyting implication is the intuitionistic logic counterpart of classical material implication, defined within Heyting algebras to capture constructive reasoning about "if–then" statements.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Brouwer–Heyting logic
Target entity description: Brouwer–Heyting logic is the standard formal system of intuitionistic logic, capturing constructive reasoning by rejecting the law of excluded middle and other non-constructive classical principles.

• 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. Heyting arithmetic
  Heyting arithmetic is a formal system of arithmetic based on intuitionistic logic, serving as the constructive counterpart to classical Peano arithmetic.
• C. 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.
• D. 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.
• E. Heyting implication
  Heyting implication is the intuitionistic logic counterpart of classical material implication, defined within Heyting algebras to capture constructive reasoning about "if–then" statements.
• F. None of above. chosen