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natural logic

Tags: nlp

monotonicity

  • key phoneoma that natural logic attempts to capture
  • substituting a phrase has predictable entailment relationships
    • example:
      • a reptile moved -> upward monotone
        • if we replace a superset with a subset, it’s entailed
        • a reptile moved -> a turtle moved
      • no reptile moved -> downward monotone
        • no turtle moved -> replacing a superset with a subset, negation has flipped the monotone
      • non-montone: do no preserve entailment in either direction

langauge

  • upward monotone is sort of the default for lexical items
  • i.e. most determiners (a, some, at least), second argument of every (danced in every), etc
  • downward monotone is usually negation, first argument of every, determiners like most, few, conditional antecedents (if-clauses), etc

limitations

  • de morgan’s laws cannot be parsed by natural logic