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An introduction to ANAPHORA and Quantification

An introduction to ANAPHORA and Quantification. Syntax and Interpretation Genève, 2010. Two conceptions of semantics.

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An introduction to ANAPHORA and Quantification

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  1. An introduction to ANAPHORA and Quantification Syntax and Interpretation Genève, 2010

  2. Two conceptions of semantics • Morris 1938: canonical division into syntax, semantics and pragmatics. According to this view, semantics is concerned with the relationship among linguistic expressions and objects/individuals of the world 2. Conceptual semantics (Jackendoff): semantics is concerned with a special kind of expressions/representations that characterize a specific status of the mind/brain

  3. Chomsky: semantics does not involve a direct relation with the external world Criticism of the notion of reference: linguistic expressions refer to the objects of the world, but this happens “from the perspective of specific human interests and objectives, and with curious properties” (Nuovi orizzonti, 73). “…un’unità lessicale ci fornisce una certa gamma di prospettive per guardare a quelli che consideriamo oggetti del mondo, o che concepiamo in modi diversi; queste unità lessicali sono come filtri o lenti che ci mettono a disposizione modi per guardare alle cose e pensare ai prodotti della nostra mente. I termini stessi non hanno riferimento, perlomeno se il termine riferimento è utilizzato con il senso che ha nel linguaggio naturale; ma le persone possono utilizzare i termini per riferirsi alle cose, guardandole da particolari punti di vista (i quali, come si è già osservato, sono assai lontani dalla prospettiva adottata nelle scienze naturali (95)

  4. Some examples to show that the notion of “reference” is problematic • Il libro che sto scrivendo peserà almeno 5 chili se sarà mai pubblicato • London is so unhappy, ugly, and polluted that it should be destroyed and rebuilt 100 miles away • John is painting the house brown • Se vedo una casa, vedo la superficie esterna; se sono in un aereo, lo vedo solo se guardo fuori dal finestrino e vedo la superficie dell’ala (94)

  5. The nature of semantic computations • Chomsky: Semantic representations are part of syntax and consist in the manipulation of symbolic objects. • The point of view that I will take: Semantic computations are distinct from syntactic computations and involve the use of a set-theoretic apparatus that relates linguistic expressions to objects in a model. What counts here are the logical and mathematical properties of those objects whereas the non-formal properties are disregarded.

  6. Semantic computations and pronominal anaphora • Pronouns as bound variables: the constraints on pronominal anaphora are NOT constraints on coreference • Semantics and language acquisition: Delay in the acquisition of Principle B of Binding Theory

  7. Bound variables readings • Every student thinks that Mary likes him • x (x thinks that Mary likes x) • The professor who tested every student thinks that Mary likes him • *x (the professor who tested x thinks che Mary likes x (5) The professor who tested no student thinks that Mary likes him (6) *x (the professor who did not test x thinks that Mary likes x) (7) The professor who did not test Charles thinks that Mary likes him (8) The professor who tested him thinks that Mary likes no student • *x (the professor who tested x thinks thatMary does not like x) (10) The professor who tested him thinks that Mary does not like Charles CONCLUSIONE: C-command is relevant for bound variable readings, but is irrelevant for coreference

  8. Properties and functions ¶Tito sleeps¶ The interpretation takes place according to a certan number of parameters (time, assignment function, world, etc.) ¶Tito¶ = t ¶sleeps¶ = [a, b, c, d…] Sleeps (x) = V/F x [x  sleep’] x [x  sleep’] (t) = [t  sleep’]

  9. Semantic tipes • f <e,t> = properties (N, V, A) • f <e,e> = mother of • f <t,t> = negation • f <e, <e,t>> = transitive verbs • f <<e,t>, <e,t>> = antonyms, modifiers… • f <<e,t>, t> = quantifiers

  10. Individuals as set of properties • x y P [[P(x)  P(y)]  x = y] • x y P [ x = y  [P(x)  P(y)] ¶Tito¶ = P<e,t> [t  P] ¶Tito sleeps¶ = 1 iff ¶Tito¶  ¶sleeps¶ ¶Tito sleeps¶ = 1 iff ¶sleeps¶  ¶Tito¶

  11. Quantifiers • Every soldier dreamed • Some soldier dreamed 3. No soldier dreamed 4. x [soldier’(x)  dreamed’(x)] 5. x [soldier’(x)  dreamed’(x)] • x [soldier’(x)  dreamed’(x)] • [[every soldier] dreamed] • [every [soldier dreamed]]

  12. Generalized quantifiers 1. ¶every soldier¶ = P<e,t> [soldier’  P] 2. ¶some soldier¶ = P<e,t> [soldier’  P ] 3. ¶no soldier¶ = P<e,t> [soldier’  P = ] ¶every soldier sleeps¶ = ¶every soldier¶ (¶sleeps¶) P<e,t> [soldier’  P] <<e,t>, t> (sleeps’ <e,t>) = soldier’  sleeps [ [every? soldier<e,t>]<<e,t>,t> sleeps<e,t>] 5. ¶every¶ = PQ [P  Q] 6. ¶some¶ = PQ [P  Q ] 7. ¶no¶ = PQ [P  Q = ]

  13. Exercises • Express 1-3 (previous slide) in terms of first-order logic notation • Give the semantics of “exactly two” • Give the semantics of “most”

  14. C-command and coreference • Every student likes him • Charles loves him QUESTION: Is Principle B a constraint on BINDING or a constraint on COREFERENCE? (3) Genève is loved by its inhabitants, Verona is not (4) Genève [x (x è amata dagli abitanti di x)] Verona [x (x non è amata dagli abitanti di x)] (5) The people who live in Geneva love it, but the people who live in Verona do not (6) Genève [x (the people living in x love x)] *Verona [x (the people living in x do not love x)] CONCLUSIONE: The bound variable reading is possible with proper names as well. It is then possible that the constraint on (2) concerns the bound variable reading and NOT coreference

  15. “Oscar-sentences” and coreference • It’s not true that Michael loves nobody! He loves Michael (2) It’s not true that nobody likes Michael! Michael likes him

  16. Crossover and Condition C • Who does he like? • Who does his professor like? • He loves everyone’s mother • His mother loves everyone • Someone loves everyone’s mother QUESTION: Why has the trace of the operator (wh-phrase or quantifier) to c-command the pronoun? COROLLARY: Why does semantic binding entails syntactic binding in natural language?

  17. Syntactic and Semantic binding  binds  if  c-commands  and  is coindexed with . Let  be a branching node with daughters  and , where  dominates only a numerical index i. Then, for every variable assignment g, ||||g = x. ||||g: i  x  QP ||||g = x. ||||g: i  x 1 t1 …i….

  18. Two ideas of anaphoric dependence 1. CLP: If x depends on y, then y has to c-command x Under CLP indexes produce only BVRs and coreference is accidental covaluation. Grammatical principles (BT principles) express constraints on the BVR. 2. INP: If x depends on y, then x cannot c-command y Under INP anaphoric dependencies are encoded through an asymmetric relation of linking. Grammatical principles constrain linking. Covaluation of two DPs is linking. 3. Both CLP and INP must be supplemented by an Obviation Rule stating that two DPs that exclude coindexation or linking as a result of grammar cannot be covalued (Reinhart’s Rule I and Safir’s Obviation) 4. John saw him 5. John said that he saw him

  19. The delay in the acquisition of Principle B (Grodzinsky&Reinhart 1993, Baauw&Delfitto 2005) • a. The boy touched him (around 50% adult-like) b.The boy touched himself (almost 100% adult-like) • Every boy touched him (85% adult-like) • La niña la señala (90% adult-like) • a. Do you know what Mary and John have in common? Mary admires him and John admires him too • Zelda’s husband is him • A. Is this speaker Zelda? B. How can you doubt it? She praises her to the sky. No competing candidate would do that • It is not really true that everyone likes John. JOHN does not like him!

  20. Clitici pronominali come variabili: dislocazione a sinistra e familiarità • Questo libro l’ho già letto 1’. Questo libro [x (ho già letto x)] • L’ho già letto 2’. [TOPe] [x (ho già letto x)] • Ognuno pensa che Maria lo ami 3’. Ognuno [x (x pensa che Maria ami x)]

  21. Quantificazione e scope • Ogni studente legge • OGNI [studente] [legge] • Leo incontra ogni studente Domanda: Qual è il secondo insieme della relazione? • [Ogni studente] [Leo incontra x] • OGNI [x: studente] [x: Leo incontra x] • Il professore che ha promosso ogni studente è impazzito • *Quale studente il professore che ha promosso è impazzito?

  22. Quantificazione e calcolo predicativo • Ogni studente legge • x [studente(x)  legge(x)] • Most students read • Most x [student(x)  read(x)] Si consideri un modello composto da 10 persone, di cui 6 leggono. Di queste 10 persone, 5 sono studenti. Dei 5 studenti, 1 legge e 4 non leggono. In questo modello, si dimostra che (4) è vera e che (3) è falsa. Quindi (4) non rappresenta una forma logica adeguata per (3)

  23. Proprietà logiche della quantificazione • Ogni A = XU/AX • Qualche A = XU/AX • Most A = XU/AXA-X • Nessun A = XU/AX= ISOMORFISMO: L’interpretazione di D è indifferente alle permutazioni degli individui di U. I determinanti sono indifferenti alle proprietà o individui particolari DOMANDA: Dimostrare che Qualche(A) è B  Qualche(f(A)) è f(B), indipendentemente dalla caratterizzazione di f

  24. Quantificazione e conservatività CONSERVATIVITA’: D(A) è B  D(A) è AB • Qualche uomo corre  Qualche uomo è un uomo che corre • La maggior parte degli uomini corre  La maggior parte degli uomini sono uomini che corrono RELAZIONI NON-CONSERVATIVE: • A = B è vero sse A = AB (identità) • <X,Y>: X>Y (quantificatore di Rescher) • Solo gli uomini fumano  solo gli uomini sono uomini che fumano • Solo A è B  AB Ma SOLO non è un determinante, ha invece la distribuzione di un avverbiale

  25. MONOTONICITA’ • Ogni studente ha lasciato la festa prima delle 10 • Ogni studente ha lasciato la festa prima delle 11 • Nessuno studente ha lasciato la festa prima delle 10 • Nessuno studente ha lasciato la festa prima delle 9 • *Every student saw any professor • No student saw any professor • Every student who praised any professor succeeded • *Every student who succeeded praised any professor • Every student who left before 10 passed the exam • Every student who left before 9 passed the exam

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