1Exclusive interpretations via scalarimplicatures?LING 610Angelika KratzerOctober 3, 20072Question• What is it about or that can bring about anexclusive interpretation?• Today’s topic: Deriving exclusiveinterpretations of disjunctions as scalarimplicatures.3Defeasibility• The exclusive interpretation we perceive in (1) is notdelivered by the regular semantic component. It canbe cancelled without contradiction.(1) The boss is away or the secretary is sick, or both.4The meanings we perceive are the result ofinteracting componentsMeanings delivered by the regular semanticsDefeasible pragmatic strengthening5A conversational implicatureaccount of exclusive interpretations6H. Paul Grice1913 - 1988• Sketch of an influentialtheory of pragmaticstrengthening: the theory ofconversational implicatures.• 1967 William James Lectureson Logic and Conversation.Published in 1989 in: Studiesin the Way of Words.Cambridge/Mass. (HarvardUniversity Press).7Laurence R. Horn• 1972 UCLA Dissertation: On the SemanticProperties of Logical Operators in English.• Horn scales can be used to generate a space ofrelevant stronger competitors to be compared towhat was literally said. A cooperative speaker’schoice of a weaker alternative might signal to thehearer that the speaker did not have sufficientevidence for the stronger alternative.8Grammaticizing alternatives via HornScales<and, or><all, many, some><no, few><always, often, sometimes><never, rarely><must, may><… three, two, one>9Back to our sentence(1) The boss is away or the secretary is sick.• Can we derive the perceived exclusiveinterpretation of (1) as a conversationalimplicature via the Horn scale <and, or>?10Relevant alternatives• (1) evokes (2) as a relevant scalar alternative.(1) The boss is away or the secretary is sick.(2) The boss is away and the secretary is sick.11Comparing Strength(2) is stronger than (1). That is, (2) is more informativethan (1).(1) The boss is away or the secretary is sick.(2) The boss is away and the secretary is sick.12A remnant of Gricean reasoningYou assume that I picked the strongest relevantalternative that I was able to put forward withoutviolating the maxim of Quality, and thus conclude thatI didn’t have sufficient evidence to maintain that theboss is away and the secretary is sick.13But not yet the exclusiveinterpretation!• I said that the boss is away or the secretary is sick.• You can only infer that I didn’t have sufficientevidence to maintain that the boss is away and thesecretary is sick. You can’t infer that my evidencewas sufficient to eliminate the possibility that bothdisjuncts are true.14A stronger conclusion?• Is there some plausible way of deriving the exclusiveinterpretation of disjunctions as a scalar implicature?It seems that we have to look at contexts thatsupport the additional assumption that my evidenceis not only sufficient to support the claim I made,but is also sufficient to exclude the strongeralternatives to my claim. What would such contextslook at?15Grammaticizing Grice?16A Grice machine?• Might there be a computational mechanismthat is part of the human language faculty andgenerates defeasible strengthenedinterpretations in a fully mechanical way?17A Grice machine?• Chierchia 2004: "Scalar Implicatures, Polarity Phenomenaand the Syntax/Pragmatics Interface" in A. Belletti (ed)Structures and Beyond, Oxford University Press, 2004.• A two-dimensional system where scalar alternatives aregenerated along with regular meanings, and are used tocompute strengthened meanings in a mechanical and fullycompositional way.18Practicing some formal notions19Strength• What does it mean that proposition A isstronger than proposition B?• Proposition A is stronger than proposition Bif and only if A logically implies B, but notthe other way round.20Visualizing StrengthA is true B is trueA is falseB is trueA is trueB is falseA or B21Visualizing StrengthA is true B is trueA and B22Visualizing StrengthA is falseB is falseNot (A or B)23Visualizing StrengthA is falseB is trueA is trueB is falseA is falseB is falseNot (A and B)24Comparing StrengthA is true B is trueA is falseB is trueA is trueB is falseA is falseB is falseA or BA & BNot(A or B)Not (A & B)25Strength & informativity• A proposition gets stronger, hence moreinformative, the more possible situations itexcludes.26Embedding disjunctions andcomparing strength27Comparing strength• They didn’t exaggerate or lie to you.• They didn’t exaggerate and lie to you.• Which of the two statements is stronger? Is orin the first sentence perceived as inclusive orexclusive?28Which paraphrase is right?• They didn’t exaggerate or lie to you.(a) They neither exaggerated nor lied to you. They didneither one of those things.(b) If they exaggerated or lied to you at all, then theydid both of those things.29Comparing strength• No more than 3 children wore hats or scarves.• No more than 3 children wore hats and scarves.• Which of the two statements is stronger? Is or in thefirst sentence perceived as inclusive or exclusive?30Which paraphrase is right?• No more than 3 children wore hats or scarves.(a) We are counting the number of all those children whowore a hat, or a scarf, or both. That number is smaller orequal to 3.(b) We are counting the number of all those children whowore a hat or a scarf, but not both. That number is smalleror equal to 3.31Comparing strength• If they abused or neglected their children, theirparental rights must be terminated.• If they abused and neglected their children, theirparental rights must be terminated.• Which of the two statements is stronger? Is or in thefirst sentence perceived as inclusive or exclusive?32Which paraphrase is right?• If they abused or neglected their children, theirparental rights must be terminated.(a) Parental rights must be terminated if they abusedtheir children, if they neglected them, and also ifthey did both.33Or this paraphrase?• If they abused or neglected their children, their parentalrights must be terminated.(b) If they abused their children, their parental rights must beterminated, as long as they didn’t neglect them as well.Likewise, if they neglected their children, their parentalrights must be terminated, as long as they didn’t abusethem as well.34Generalization• We seem to observe the exclusive reading ofor in precisely those contexts where thecorresponding and statement expresses astronger proposition.35Support for the