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Entailment relations

Containment, Exclusion and Implicativity : A Model of Natural Logic for Textual Inference ( MacCartney and Manning). Every firm saw costs grow more than expected, even after adjusting for inflation Every privately held firm saw costs grow

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Entailment relations

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  1. Containment, Exclusion and Implicativity: A Model of Natural Logic for Textual Inference (MacCartney and Manning) • Every firm saw costs grow more than expected, even after adjusting for inflationEvery privately held firm saw costs grow • Natural logic: “characterizes valid patterns of inference in terms of syntactic forms resembling natural language • In ordinary upward monotone contexts, deleting modifiers preserves truth • In downward monotone contexts, inserting modifiers preserves truth • Every is downward monotone

  2. Entailment relations • Equivalence (couch = sofa) • Forward entailment (crow -> bird; European <- French) • Negation or exhaustive exclusion (human and non-human) • Alternation or non-exhaustive exclusion (cat | dog) • Cover or non-exclusive exhaustion (animal * nonhuman) • Independence (hungry # hippo)

  3. Projectivity Class Categorize semantic functions by projectivity class: • The projectivity class of f: how the entailment relation of f(x) and f(y) depends on the entailment relation of x and y • Not: • Projects = and # with no change • Not happy = not glad • Isn’t swimming # isn’t hungry • Swaps -> and <- • Didn’t kiss <- didn’t touch • Projects exhaustion without change • Not human and not inhuman • Swaps | and * • Not French * not German • Not more than 4 | not less than 6

  4. Refuse and projectivity • Swaps -> and <- • Refuse to tango <- refuse to danse • Projects exhaustion as alternation • Refuse to stay | refuse to go • Projects both | and * as # • Refuse to tango # refuse to waltz

  5. Full example • I can’t live without mangos • (not (((without mangos) live) I)) • Mangos -> fruit • Without is downward monotone, without mangos <- without fruit • Not downward monotone, I can’t live without mangos -> I can’t live without fruit.

  6. Implicatives: 9 implication signatures • Positive (+), negative (-), null (°) in positive, negative contexts • Refuse • -/°: • a negative implication in a positive context • Refused to danse -> didn’t danse • no implication in a negative context • Didn’t refuse to danse implies neither dansed or didn’t danse

  7. Modeled through composition and edits (deletions) • -/° (refuse) generates | • Jim refused to dance | Jim danced • Under negation, projected as exhaustive exclusion: • Jim didn’t dance , Jim refused to dance • °/- (attempt) generates <- • Jim attempted to dance <- Jim danced • Under negation projected as -> • Jim didn’t attempt to dance -> Jim didn’t dance

  8. Architecture • Linguistic analysis • Parsing • Projectivity marking • Alignment • Lexical entailment classification • Entailment projection • Entailment composition

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