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