1. Optimality Theory and Pragmatics Lecture series in three parts held at the V. Mathesius Center, Prague, March 2004 Part 2: M-Implicatures and Weak Optimality Manfred Krifka Humboldt University Berlin Center for General Linguistics (ZAS), Berlin Copy of presentation at: http://amor.rz.hu-berlin.de/~h2816i3x

2. Things to Do: 1. The Classic Theory of Implicatures: Grice 2. Optimality Theory 3. An OT Account of Scalar Implicatures 4. The Theory of I/R Implicatures: Horn, Levinson 5. Strong Bidirectional Optimality Theory Accounts of blocking, pronoun interpretation, freezing of word order 6. The Theory of M Implicatures: Levinson 7. Weak Bidirectional OT Account of Partial Blocking 8. Weak Bi-OT Account of Measure Term Interpretation 9. An OT account of Scale Alignment 10. Functional motivation for linguistic scales 11. Stochastic OT 12. Bidirectional OT account of Learning 13. Bidirectional OT account of Language Change: 14. Differential Case Marking

3. Recapitulation: Q-Implicature / I-Implicature Q-Principle: Say as much as you can. Explains implicatures that restrict what is said to the literal meaning. Example: Scalar implicatures. John has three children. restricted to: John doesn’t have more than three children. I-Principle: Say (only) as much as you must. Explains implicatures that enrich the literal meaning of what is said. Example: Bridging.. Bill unpacked the picknick. The beer was warm. enriched to: The beer that was part of the picknick was warm.

4. The M Principle Levinson (2000) assumes a third principle beyond Q and I: Q-Principle: Speaker: Choose the maximally informative expression alternative (that still is true). Addressee: Assume that speaker has chosen the maximally informative expression alternative (that still is true) I-Principle: Speaker: Produce only as much linguistic information as necessary to satisfy the communicative purpose. Addressee: Enrich the given linguistic information, identify the most specific information relative to the communicative purpose. M-Principle (Modality / Manner / Markedness) Speaker: Communicate non-normal, non-stereotypical situations by expressions that contrast with those that you would choose for normal, stereotypical situations. Adressee: If something is communicated by expressions that contrast with those that would be used for normal, stereotypical meanings, then assume that the speaker wants to communicate a non-normal, non-stereotypical meaning.

5. M-Implicatures and I-Implicatures If the speaker utters an expression A[M], which contains a marked expression M with meaning B, Literal meaning of M / U Restriction by I-Implicature if U is used. Restriction by M-Implicature if M is used. and if there is an unmarked expression U with similar meaning M, and the speaker could have said A[U], where A[U] would have triggered an I-Implicature, that U should be understood with the specialized meaning b then the speaker implicates with A[M] that M is to be understood as the complement b in B.

6. M-Implicatures: To Kill and to Cause to Die Generative Semantics: Syntactic treatment of lexical semantics: [kill] = [cause [to die]] [die] = [become [not [alive]]] [open transitive ] = [cause [to open intransitive ]] But McCawley (1978): Different interpretations of Black Bart killed the sheriff. Direct killing. Black Bart caused the sheriff to die. Indirect killing. Mary opened the door.Normal, stereotypical opening. Mary caused the door to open.Non-normal, atypical opening. Explanation by M-Implicature: literal meaning of kill / cause to die Restriction by I-Implicature for unmarked kill to direct killing. Restriction by M-Implicature for marked cause to die to indirect killing.

7. M-Implicature: Of Old Men and Elderly Men (1) John is an old man. (2) John is an elderly man. English speakers understand (1) as indicating a higher age than (2), cf. the dictionary definition: elderly: being past middle age and approaching old; rather old. Assume: old (for people) and elderly literally mean the same: Older than average (general principle of interpretation fo gradable adjectives in positive form) but elderly is marked, which leads to an M-Implicature. Age old / elderly: literal meaning old: I-Implicature elderly: M-Implicature

8. Other Examples of M-Implicatures Miss X sang “Home Sweet Home”. I-Implicature: Miss X sang “Home Sweet Home” in a normal way. Miss X created a series of sounds that corresponded quite closely to the notes of “Home Sweet Home” M-Implicature: Miss X sang “Home Sweet Home” in a non-normal way. Karen smiled. I-Implicature: Karen smiled in a regular way.. Karen lifted the corners of her lips. M-Implikature: Karen produced an aritificial smile. Linda went to the library and copied an article. I-Implicature: She first went to the library and then copied an article. Linda went to the library, and she also copied an article. M-Implikature: No claim about the order in which this happened.

9. M-Implicatures: The Meaning of Reduplications Reduplications increase the complexity of expressions and can trigger M-Implicatures. He went to bed and slept. I-Implicature: prototypical sleeping. He went to bed and slept and slept. M-Implikatur: Non-prototypical, long sleeping; iconic marking: repetition of expression - repetition / lengthening of event. Often, reduplication means higher length or intensity, but not always: In Africans, reduplication can mean to do try to do something’ skop ‘kick’, skop-skop ‘try to kick’, ‘kick in an experimental way’ In Western Desert, Australia, similar meaning for nouns: wati ‘men, wati-wati ‘boys that claim to be men’ In Mayan languages (e.g. Tzeltal): Simple color terms: focal colors Reduplicated color words: non-focal color, like red - reddish In general: reduplicated forms are more complex and denote non-typical situations or entities compared to simplex forms.

10. M-Principle and Bidirectional OT Levinson assumes that the M-Principle is a separate principle. But it is tightly connected to other principles. Black Bart killed the sheriff. Literal interpretation: brought it about that the sheriff died Enrichment by I-Implicature: in a direct way Black Bart caused the sheriff to die Literal interpretation: brought it about that the sheriff died No enrichment by I-Implicature, presumably because killed the sheriff shows this enrichment. Restriction to brought it about that the sheriff died, presumably because of contrast with I-Implicature to killed the sheriff. To explain: Why does only killed the sheriff show I-Implicature? Why does interpretation of caused the sheriff to die contrast with I-Implicature of killed the sheriff ?

11. Recapitulation: Strong Bidirectional OT Evaluation algorithm for strongly optimal form-meaning pair:  F, M  is strongly optimal iff a.  F, M   GEN, that is,  F, M  is generated. b.there is no  F’, M   GEN such that  F’, M  >  F, M  c.there is no  F, M’   GEN such that  F, M’  >  F, M  where P 1 > P 2 means: P 1 is preferred over P 2. cheaper more cheap cheap  cheaper, cheap  >  more cheap, cheap , simplicity of expression Mary wrote the novel on a computer. ‘Mary wrote the novel by means of a computer’ ‘Mary wrote the novel while she was on a computer’  Mary wrote..., by means  >  Mary wrote..., while on , stereotypicality of meaning

12. Strong Bi-OT and Kill / Cause to Die kill cause to die cause death in direct way cause death in indirect way Speaker optimization: select simpler expression Hearer optimization: select stereotypical meaning kill cause to die cause death in direct way cause death in indirect way combined Speaker + Hearer optimization  kill, cause death in direct way  is the only strongly optimal pair; it is better than  kill, cause death in indirect way ,  cause to die, cause death in direct way ,  cause to die, cause death in indirect way  No way to express marked meaning (“ineffability”), complex epressions are always blocked (“uninterpretabiity”)

13. Weak Bidirectional OT Recall strong optimality:  F, M  is strongly optimal iff a.  F, M   GEN, that is,  F, M  is generated. b.there is no  F’, M   GEN such that  F’, M  >  F, M  c.there is no  F, M’   GEN such that  F, M’  >  F, M  Alternative notion of weak optimality (Blutner 2000, Jäger 2002):  F, M  is weakly optimal iff a.  F, M   GEN, that is,  F, M  is generated. b.there is no weakly optimal  F’, M   GEN such that  F’, M  >  F, M  c.there is no weakly optimal  F, M’   GEN such that  F, M’  >  F, M  Infelicitous definition because definiens occurs in definiendum? This is only apparent!

14. Weak Bi-OT and Kill / Cause to Die Generated alternatives GEN to consider: {  kill, cause death in direct way ,  cause to die, cause death in direct way   kill, cause death in indirect way ,  cause to die, cause death in indirect way  } First step:  kill, cause death in direct way  is weakly optimal because there is no weakly optimal (in fact, no)  F’, cause death in direct way   GEN and no weakly optimal (in fact, no)  kill, M’   GEN that is preferred over  kill, cause death in direct way  Second step:  kill, cause death in indirect way  is not weakly optimal, as  kill, cause death in direct way  is weakly optimal and preferred. Third step:  cause to die, cause death in direct way  is not weakly optimal, as  kill, cause death in direct way  is weakly optimal and preferred. Fourth step:  cause to die, cause death in indirect way  is weakly optimal (!) because there is no weakly optimal  F’, cause death in indirect way   GEN and there is no weakly optimal  kill, M’   GEN that is preferred over  cause to die, cause death in indirect way 

15. Weak Bi-OT and Kill / Cause to Die  kill, cause death in direct way   cause to die,  kill, cause death in direct way  cause death in indirect way ,  cause to die, cause death in indirect way  Notice:Partial blocking; the marked form is not blocked under the marked interpretation - the “emergence of the marked”

16. Weak Bi-OT and Kill / Cause to Die kill cause to die cause death in direct way cause death in indirect way Speaker optimization: select simpler expression Hearer optimization: select stereotypical meaning kill cause to die cause death in direct way cause death in indirect way combined Speaker + Hearer optimization: optimal (and weakly optimal) solution kill cause to die cause death in direct way cause death in indirect way combined Speaker + Hearer optimization: additional weakly optimal solution, prevents ineffability and uninterpretability

17. Weak Bi-OT on Being Elderly  old man, prototypically old   elderly man,  old man, prototypically old  non-prototypically old ,  elderly man, non-prototypically old 

18. A Kafkaesque Account of Strong and Weak Bidirectional OT In his early prose piece Die Abweisung (“Turned Down”) Franz Kafka imagines a dialogue between himself and a young woman: "Du bist kein Herzog mit fliegendem Namen, kein breiter Amerikaner mit indianischem Wuchs, mit wagrecht ruhenden Augen, mit einer von der Luft der Rasenplätze und der sie durchströmenden Flüsse massierten Haut. Du hast keine Reisen gemacht zu den großen Seen und auf ihnen, die ich weiß nicht wo zu finden sind. Also ich bitte, warum soll ich, ein schönes Mädchen, mit Dir gehn?” In short: Woman says to man: You are not the most attractive man. "Du vergißt, Dich trägt kein Automobil in langen Stössen schaukelnd durch die Gasse, ich sehe nicht die in ihre Kleider gepressten Herren Deines Gefolges, die Segensprüche für Dich murmelnd in genauem Halbkreis hinter Dir gehn; Deine Brüste sind im Mieder gut geordnet, aber Deine Schenkel und Hüften entschädigen sich für jene Enthaltsamkeit; Du trägst ein Taffetkleid mit plissierten Falten, wie es im vorigen Herbste uns durchaus allen Freude machte, und doch lächelst Du - diese Lebensgefahr auf dem Leibe - bisweilen.” In short: Man says to woman: You are not the most attractive woman. Kafka’s ending is an example of Strong Optimality: Woman and man go home alone. " Ja, wir haben beide recht und, um uns dessen nicht unwiderleglich bewusst zu werden, wollen wir, nicht wahr, lieber jeder allem nach Hause gehn.” Krifka’s variant, an example of Weak Optimality: Woman and man go home together because other pairings would not be stable. “Ja, wir haben beide recht. Doch wenn Du Deine Prinzessin finden würdest, wärest Du nie sicher, wie lang sie bei Dir bleiben würde. Und wenn mir mein Held erschiene, würde er mich auch nur eines Blickes würdigen? So lass uns zusammen nach Hause gehen.

19. Weak Bi-OT on Being not Unhappy Larry Horn (1991), Duplex negatio affirmat: The economy of double negation. Mary is not unhappy implicates: Mary is not really happy.  Initial situation: Contrary (antonymic) pairs of expressions and their negations. not unhappynot happy happyunhappy I-Implicatures: Restriction of simpler expressions to prototypical uses.  not unhappynot happy happyunhappy  not unhappynot happy happyunhappy M-Implicatures: Restriction of complex expressions to non-prototypical uses.

20. Weak Bi-OT on Being not Unhappy  happy,   not unhappy,  happy,   not unhappy,   unhappy,    not happy,   unhappy,    not happy,   Cf. also: This is good. This is bad. This is not bad. This is not good.

21. An Alternative Theory about Happiness? Speakers generally have the impression that the literal meanings of happy and unhappy are different:  happyunhappy Problem with this view: Unclear how to derive the different uses of not happy and not unhappy  happyunhappy not unhappy not happy Strengthening by M-Implicature:  happyunhappy not unhappy not happy Unclear how different interpretation of not happy an d not unhappy comes about, prediction: not unhappy should be totally blocked because it is longer than not happy!

22. A New Type of Blocking: Saussure on Plural and Dual A type of blocking not considered so far: “The value of a German or Latin plural is not the value of a Sanskrit plural. But the meaning, if you like, is the same. In Sanskrit, there is the dual. Anyone who assigns the same value to the Sanskrit plural as to the Latin plural is mistaken because I cannot use the Sanskrit plural in all the cases where I use the Latin plural.” (Saussure, Notes taken by student, July 4, 1911) 1234... Plural Latin DualPlural Sanskrit Idea: Plural in Sanskrit has the same “meaning” as plural in Latin, but it is blocked when applied to the number 2 by the Dual, hence their “values” are different.

23. Bi-OT on Dual and Plural Consider form-meaning pairs like the following:  Dual, 2   Plural, 2   Plural, 3   Plural, 4  Which constraints should we assume here? Form constraints? Dual may be more complex than plural and hence dispreferred, but meaning 2 doesn’t appear to be a marked meaning, and hence dual may be blocked in general! Also, a consideration of speaker vs. hearer perspective doesn’t help: Dual Plural 234234 Hearer perspective Dual Plural 234234 Speaker perspective Dual Plural 234234 Common perspective

24. Bi-OT on Dual and Plural But notice that the pair  Dual, 2  is special, as a dual form cannot denote any other numbe;: it is unambiguous. Proposal: Give preference to pairs  F, M  with forms F that cannot express any other meaning, that is, for which there is no  F, M’   GEN with M’  M. Avoid ambigous forms (AAF):  F, M  >  F’, M  if F is unambigous. It follows that  Dual, 2  >  Plural, 2 , hence  Plural, 2  is excluded by optimality priciples. Notice: AAF is not a principle that can be reduced to forms (like: prefer simple expressions) or that can be reduced to meanings (like: prefer stereotypical meanings) Dual Plural 234234 Avoid Ambiguity.

25. Avoid Ambiguous Forms and Weak Bi-OT There is a connection between AAF and Weak Bi-OT; AAF is a simplified evalution algorithm. Recall definition of weak optimality:  F, M  is weakly optimal iff a.  F, M   GEN b.there is no weakly optimal  F’, M   GEN such that  F’, M  >  F, M  c.there is no weakly optimal  F, M’   GEN such that  F, M’  >  F, M  With partial blocking of plural by dual, alternative form/meaning pairs are not comparable:  Dual, 2   Plural, 2 , if dual and plural are equally complex. Asymmetric optimality:  F, M  is asymmetrically optimal iff a.  F, M   GEN, b.(does not apply) b.there is no  F, M’   GEN different from  F, M . We have that  Dual, 2  is asymmetrically optimal, as there is no  Dual, n , n  2; but  Plural, 2  is not asymmetrically optimal, as we have, e.g.  Plural, 3 .

26. Bi-OT and other numbers Similar reasoning applies to singular and plural in English. General meaning of plural includes single cases: Do you have children? Yes, I have one. / *No, I have (only) one. Do you have more than one child? No, I have only one. / *Yes, I have one. But in competition with singular, plural is blocked if meaning 1 is encoded. Singular Plural 123123 Application to Paucal / Plural systems, e.g. Arabic: Paucal is used for small numbers, e.g. under 4, Plural is used elsewhere. Avoid Ambiguity, generalized:  F, M  >  F’, M  if F is less ambiguous than F’.

27. Bi-OT and Measure Expressions From the land of bankers and watchmakers. Street sign in Kloten, Switzerland.

28. Pedantic and helpful answers. A:The distance between Amsterdam and Vienna is one thousand kilometers. B:#No, you’re wrong, it’s nine hundred sixty-five kilometers. A:The distance between A and V is nine hundred seventy-two kilometers. B:No, you’re wrong, it’s nine hundred sixty-five kilometers. A:The distance between A and V is one thousand point zero kilometers. B:No, you’re wrong, it’s nine hundred sixty-five kilometers. A:Her phone number is sixty-five one thousand. B:No, her phone number is sixty-five one-thousand and one. The distance between A and V is roughly one thousand kilometers. The distance between A and V is exactly one thousand kilometers. The distance between A and V is exactly nine hundred sixty-five kilometers. #The distance between A and V is roughly nine hundred sixty-five kilometers.

29. Pedantic and helpful answers. A:The distance between Amsterdam and Vienna is one thousand kilometers. B:#No, you’re wrong, it’s nine hundred sixty-five kilometers. A:The distance between A and V is nine hundred seventy-two kilometers. B:No, you’re wrong, it’s nine hundred sixty-five kilometers. A:The distance between A and V is one thousand point zero kilometers. B:No, you’re wrong, it’s nine hundred sixty-five kilometers. A:Her phone number is sixty-five one thousand. B:No, her phone number is sixty-five one-thousand and one. The distance between A and V is roughly one thousand kilometers. The distance between A and V is exactly one thousand kilometers. The distance between A and V is exactly nine hundred sixty-five kilometers. #The distance between A and V is roughly nine hundred sixty-five kilometers.

30. Precision level and rounded numbers Precision Level Choice: When expressing a measurement of an entity, choose a precision level that is adequate for the purpose at hand. Oddness explained: Change in precision level. A:The distance between Amsterdam and Vienna is one thousand kilometers. B:#No, you’re wrong, it’s nine hundred sixty-five kilometers. Round Numbers / Round Interpretations (RN/RI) Short, simple, round numbers suggest low precision levels. Long, complex numbers suggest high precision levels. The distance between Amsterdam and Vienna is one thousand kilometers. Low precision level, vague interpretation. The distance between Amsterdam and Vienna is nine hundred sixty-five kilometers. High precision level, precise interpretation. Question: How to explain RN/RI by more general pragmatic principles?

31. A Preference for Short Expressions B RIEF E XPRESSION (first formulation): Brief, short expressions are preferred over longer, complex ones. Informal explanation of RN/RI: (a)The distance between A and V is one thousand kilometers. (b)The distance between A and V is nine hundred sixty-five kilometers. Speaker prefers (a) over (b) because it is shorter, even though it has to be interpreted in a vague way.

32. A closer look at brevity A problem for brevity: (a)The distance between A and V is one thousand and one kilometers. (b)The distance between A and V is one thousand and one hundred kilometers. Note: (a) is shorter, but interpreted more precisely, than (b). (c) The train will arrive in five / fifteen / fourty-five minutes. (d)The train will arrive in four / sixteen / fourty-six minutes. Note: (c), (d) equally short, but (d) interpreted more precisely. Solution: We cannot just look at the expression used, we also have to take its alternatives into account. (a)... nine hundred ninety nine, one thousand, one thousand and one,... (b)... nine hundred, one thousand, one thousand one hundred,... Expressions in (a) are shorter/less complex on average than in (b), e.g. by morphological complexity or number of syllables. Example: (a)one, two, three, four, five,...., one hundred:Syllable average: 2,73 (b) ten, twenty, thirty, fourty, fivty,... one hundred:Syllable average: 2,1

33. A closer look at brevity B RIEF E XPRESSION (refined): Precision levels with smaller average expression size are preferred over precision levels with longer average expression size. Suggested precision level: The use of a number words in measure expressions suggests the precision level with the smallest average expression size. For example, one thousand suggests precision level... nine hundred, one thousand, one thousand one hundred,...one thousand and one suggests precision level... nine hundred ninity-nine, one thousand, one thousand and one,... Informal explanation of RN/RI (refined): (a)The distance between A and V is one thousand kilometers. (b)The distance between A and V is nine hundred sixty-five kilometers. Speaker prefers (a) over (b) because it indicate a precision level choice with smaller average precision level, even though it has to be interpreted in a vague way.

34. A preference for precise interpretations? Notice: Use of even though suggests that precise interpretations are preferred. P RECISE I NTERPRETATION: Precise interpretations of measure expressions are preferred. This explains why (a) is interpreted precisely. (a)The distance between A and V is nine hundred sixty-five kilometers. Why no precise interpretation with (b)? Because of B RIEF E XPRESSION. (b)The distance between A and V is one thousand kilometers. If distance is 965 km, then we have the following constraint interaction: Expression B RIEF E XPR P RECISE I NT (a) nine hundred sixty-five kilometers * (b) one thousand kilometers * If constraints are unranked, both (a) and (b) are possible. If B RIEF E XPR > P RECISE I NT, then (b) is preferred.

35. A preference for precise interpretations? A problem with this reasoning: Assume the distance is exactly 1000 km, then speaker doesn’t violate any constraint: Expression B RIEF E XPR P RECISE I NT one thousand kilometers So, on hearing one thousand kilometers, the hearer should assume that the distance is exactly 1000 km, as in this case there is no violation at all. But this is clearly not the case. So, the hearer should prefer vague interpretations! V AGUE I NTERPRETATION: Vague interpretation of measure terms are preferred. Assume, again, the distance is exactly 1000 km. Expression B RIEF E XPR V AGUE I NT one thousand kilometers Hearer prefers vague interpretations nevertheless.

36. Preference for Vague Interpretations Why should vagueness be preferred? Grice, Maxime of quantity, second submaxime: Give not more information than required. Ochs Keenan (1976) (rural Madagascar): Vague interpretations help save face. P. Duhem (1904), cited after Pinkal (1995): “There is a balance between precision and certainty. One cannot be increased except to the detriment of the other.” Reduction of cognitive load? Problem: Assume distance is 965 kilometers. Expression B RIEF E XPR V AGUE I NT (a) one thousand kilometers (b) nine hundred sixty-five kilometers * * (b) would always be strongly dispreferred. We have to capture the interaction between the two principles: Basic idea: We can violate one principle if we also violate the other.

37. Weak OT on Brevity and Vagueness Ranking of pairs by B(rief)E(xpression) and V(ague)I(nterpretation):  one thousand, precise > BE  nine hundred sixty five, precise ,  one thousand, vague) > VI  one thousand, precise   one thousand, vague  > BI  nine hundred sixty five, vague   nine hundred sixty five, vague  > VI  nine hundred sixty five, precise  Generalization: Finding the weakly optimal pair: An expression-interpretation pair  F, M  is weakly optimal iff there are no other weakly optimal pairs  F, M’  or  F’, M  such that  F, M’  >  F, M  or  F’, M  >  F, M 

38. Optimal expression-interpretation pairs  one thousand, precise   one thousand, vague   nine hundred sixty-five, vague   nine hundred sixty-five, precise  Non-optimal Optimal Optimal, as the other comparable pairs are non-optimal.

39. Construction of Scales and Complexity of Expressions Requirement for vagueness / brevity interaction: Construction / historical development of appropriate scales (alternatives) optimally with equidistant representations. Example: Decimal system of counting, different scales of granularity. 010203040 Scale 1 Average complexity of expressions is smaller in Scale 1 than in Scale 2 Development of intermediate scales with anchor 5 010 203040 123456789 Scale 2 Phonological simplifying of expressions of coarse-grained scales: -- English fifteen (*fiveteen), fifty (*fivety) -- Colloquial German fuffzehn (fünfzehn), fuffzig (fünfzig) 0102030405 Scale 3 15 2535

40. Things Accomplished: 1. The Classic Theory of Implicatures: Grice 2. Optimality Theory 3. An OT Account of Scalar Implicatures 4. The Theory of I/R Implicatures: Horn, Levinson 5. Strong Bidirectional Optimality Theory Accounts of blocking, pronoun interpretation, freezing of word order 6. The Theory of M Implicatures: Levinson 7. Weak Bidirectional OT Account of Partial Blocking 8. Weak Bi-OT Account of Measure Term Interpretation 9. An OT account of Scale Alignment 10. Functional motivation for linguistic scales 11. Stochastic OT 12. Bidirectional OT account of Learning 13. Bidirectional OT account of Language Change: 14. Differential Case Marking