Definites and Indefinites

1. Definites and Indefinites An introduction to two theories with non-quantificational analysis’ of indefinites

2. File Change Semantics and the Familiarity Theory of Definiteness Irene Heim Definites and Indefinites

3. Distinction between indefinites and definites • “familiarity theory of definiteness” A definite is used to refer to something that is already familiar at the current stage of the conversation. An indefinite is used to introduce a new referent. • this definition presumes that definites and indefinites are referring expressions counterexample: Every cat ate its food. Definites and Indefinites

4. Karttunen’s Discourse Referents A definite NP has to pick outan already familiar discourse referent, whereas an indefinite NP always introduces a new discourse referent. • This reformulation makes the familiarity theory immune to the objection given above Definites and Indefinites

5. But what exactly are discourse referents and where do they fit into semantic theory ? To answer this question Irene Heim introduces “file cards” (theoretical constructs similar to the discourse referents of Karttunen) Definites and Indefinites

6. Conversation and File-keeping 1a)A woman was bitten by a dog. b)She hit it. c)It jumped over a fence. Before the utterance starts, the listener has an empty file (F0). As soon as 1a) is uttered, the listener puts two cards into the file and goes on to get the following file: Definites and Indefinites

7. F1: 1 2 -is a woman -is a dog -was bitten by 2 -bit 1 Next, 1b) gets uttered, which prompts the listener to update F1 to F2: F2: 1 2 -is a woman -is a dog -was bitten by 2 -bit 1 -hit 2 -was hit by one Definites and Indefinites

8. F3: 1 2 3 -is a woman -is a dog -is a fence -was bitten by 2 -bit 1 -was jumped over -hit 2 -was hit by 1 by 2 -jumped over 3 With this illustration in mind the question, how definites differ from indefinites can be answered in the following way: For every indefinite, start a new card. For every definite, update an old one. Definites and Indefinites

9. Model of Semantic Interpretation syntactic representation logical forms file change potential files files truth conditions Definites and Indefinites

10. Files and the World • A file can be evaluated to whether it corresponds to the actual facts or misrepresents them What does it take for a file to be true? We have to find a sequence of individuals that satisfies the file e.g. A woman was bitten by a dog. <a1,a2> satisfies F1 iff a1 is a woman, a2 is a dog, and a2 bit a1 Definites and Indefinites

11. Semantic categories and logical forms Logical forms differ from surface structures and other syntactic levels of representation in that they are disambiguated in two respects: scope and anaphoric relations Some examples of logical forms for English sentences on the black-board Definites and Indefinites

12. Logical forms and their file change potential If we have a logical form p that determines a file change from F to F’, we express this by writing: F + p = F’ We discuss just one aspect of file change, namely how the satisfaction set is affected (Sat(F+p)) Definites and Indefinites

13. Let us look at the example from the beginning in a more formal way: Dom(F1) = Dom(F2) = {1,2} Sat(F1) = { <a1,a2> : a1 is a woman, a2 is a dog, and a2 bit a1} Sat(F2) = {<a1,a2> : <a1,a2> is element of Sat(F1) and <a1,a2> is element of Ext(“hit”) } Definites and Indefinites

14. In our example we focused on a particular logical form for the sentence “She hit it” namely “She1 hit it1”. But there are infinitely many others. e.g. (1) She1 hit it1. (2) She3 hit it7. (3) She2 hit it1. In order to disambiguate a sentence the current state of the file has to be taken into consideration. This is expressed in the following rule: Definites and Indefinites

15. (2)Let F be a file, p an atomic proposition. Then p is appropriate with respect to F only if, for every NPi with index i that p contains: if NPi is definite, then i is element of Dom(F), and if NPi is indefinite, then i is not element of Dom(F). But with this rule alone not all inappropriate logical forms are ruled out (e.g. gender has to be taken into account) Definites and Indefinites

16. Let us look at another example to see how the computation of logical forms that are added to a file work: “A cat arrived” logical form on the black-board Because this is a molecular proposition the processing works a little bit different than in the previous example. (1) Sat(F0 + [NP1a cat]) = {<b1>:b1 is element of Ext(“cat”)}. (2) Sat((F0 + [NP1a cat]) + [Se1 arrived]) = {<b1>:b1 is element of Ext(“cat”) and b1 is element of (“arrived”)}. Definites and Indefinites

17. Adverbs of Quantification David Lewis Definites and Indefinites

18. Cast of Characters The adverbs considered fall in six groups of near-synonyms, as follows: (1) Always, invariably, universally,... (2) Sometimes, occasionally (3) Never (4) Usually, mostly generally, (5) Often, frequently (6) Seldom, rarely, infrequently Definites and Indefinites

19. ? ? ? ? ? ? No doubt they are quantifiers. but what do they quantify over ? ? ? ? ? ? ? Definites and Indefinites

20. First Guess: Quantifiers over Time May seem plausible: Example with always: always is a modifier that combines with a sentence Φ to make the sentence Always Φ that is true iff the modified sentence Φ is true at all times The Problems: 1) Times quantified over need not be moments of time. 1.1) The fog usually lifts before noon here = true on most days, not at moments. Definites and Indefinites

21. First Guess: Quantifiers over Time 2) Range of quantification is often restricted: 1.2)Caesar seldom awoke before dawn. (restricted to the times when Caesar awoke ) 3) Entities quantified over, may be distinct although simultaneous 1.3)Riders on the Thirteenth Avenue line seldom find seats Definites and Indefinites

22. Second Guess:Quantifiers over Events It may seem that the adverbs are quantifiers, suitable restricted, over events. The time feature is included, because events occur at times. 1.1)The fog usually lifts before noon here Interpretation as events: most of the daily fog-liftings occurred before noon. The Problems: 1) 2.1) A man who owns a donkey always beats it now and then Means: Every continuing relationship between a man and his donkey is punctuated by beatings. BUT: Beatings are not events. Definites and Indefinites

23. Second Guess:Quantifiers over Events 2) Adverbs may be used in speaking of abstract entities without location in time and events 2.1) A quadratic equation has never more than 2 solutions. This has nothing to do with times or events. - one could imagine one but it couldn‘t cope with that kind of sentence: 2.2) Quadratic equations are always simple. Definites and Indefinites

24. So far no useful solutions Definites and Indefinites

25. Third Guess:Quantifiers over Cases What can be said: Adverbs of quantification are quantifiers over cases. (i.e.: they hold in some all, no most, ..., cases) What is a case?: sometimes there is a case corresponding to • each moment or stretch of time • each event of some sort • each continuing relationship between a man and his donkey. • each quadratic equation Definites and Indefinites

26. Unselected Quantifiers We make use of variables: 3.1) Always, p divides the product of m and n only if some factor of p divides m and the quotient of p by that factor divides n. 3.2) Usually, x bothers me with y if he didn‘t sell any z. When quantifying over cases: for each admissible assignment of values to the variables that occur free in the modified sentence there has to be a corresponding case. The ordinary logicians` quantifiers are selective: x or x binds the variable x and stops there. Any other variables y,z,.... that may occur free in this scope are left free. Definites and Indefinites

27. Unselected Quantifiers Unselective quantifiers bind all the variables in their scope. They have the advantages of making the whole thing shorter Lewis claims: the unselective  and  can show up as always and sometimes. But quantifiers are not entirely unselective: they can bind indefinitely many free variables in the modified sentence, but some variables - the ones used to quantify past the adverbs - remain unbound. 3.3 There is a number q such that, without exception, the product of m and n divides q only if m and n both divide q. Definites and Indefinites

28. Unselected Quantifiers But time cannot be ignored → a modified sentence is treated as if it contains a free time-variable. (i.e. truth also depends on a time coordinate) Also events can be included similar by a event-coordinate There may also be restrictions which involve the choice of variables. (e.g. participants in a case has to be related suitable) Definites and Indefinites

29. Restriction by If-Clauses There are various ways to restrict admissible cases temporally. If-clauses are a very versatile device restriction 3.4) Always, if x is a man, if y is a donkey, and if x owns y, x beats y now and then Admissible cases for the example are those that satisfy the three iff clauses. (i.e. they are triples of a man, a donkey and a time such that the man owns the donkey at the time) A free variable of a modified sentence may appear in more than one If-clause or more variables appear in one If-clause, or no variable appears in an if-clause. 3.5) Often if it is raining my roof leaks (only time coordinate) Definites and Indefinites

30. Restriction by If-Clauses Several If-clauses can be compressed into one by means of conjunction or relative clauses. The if of restrictive if-clauses should not be regarded as a sentential connective. It has no meaning apart from the adverb it restricts. Definites and Indefinites

31. Stylistic Variation Sentences with adverbs of quantification need not have the form we have considered so far (i.e. adverb + if clauses + modified sentences) This form however is canonical now we have to consider structures which can derive from it. The constituents of the sentence may be rearranged 4.1) If x and y are a man and a donkey and if x owns y, x usually beats y now and then. 4.2) If x and y are a man and a donkey, usually x beats y now and then if x owns y Definites and Indefinites

32. Stylistic Variation The restrictive if-clauses may, in suitable contexts, be replaced by when-clauses: 4.3) If m and n are integers, they can be multiplied 4.4) When m and n are integers, they can be multiplied It is sometimes also possible to use a where-clause if a if clause sounds questionable. Always if -or always when? -may be contracted to whenever a complex unselective quantifier that combines two sentences Always may also be omitted: 4.5) (always) When it rains, it pours. Definites and Indefinites

33. Displaced restrictive terms Supposing a canonical sentence with a restrictive if-clause of the form (4.6) if α is τ …, where α is a variable and τ an indefinite singular term formed from common noun by prefixing the indefinite article or some 4.7) if x is a donkey … 4.8) if x is a old, grey donkey … 4.9) if x is some donkey … τ is called restrictive term when used so. We can delete the if-clause and place the restrictive term τ in apposition to an occurrence of the variable α elsewhere in the sentence. Definites and Indefinites

34. Displaced restrictive terms 5.0 Sometimes if y is a donkey, and if some man x owns y, x beats y now and then  Sometimes if some man x owns y, a donkey, x beats y now and then Often if x is someone who owns y, and if y is a donkey, x beats y now and then  Often if x is someone who owns y, a donkey, x beats y now and then  Often if x is someone x who owns y, a donkey, beats y now and then Definites and Indefinites

35. A theory of Truth andSemantic Representation Hans Kamp Definites and Indefinites

36. Introduction Two conceptions of meaning have dominated formal semantics: • Meaning = what determines conditions of truth • Meaning = that which a language user grasps when he understands the words he hears or reads. this two conceptions are largely separated- Kamp tries to come up with a theory which unites 2 again. The representations postulated are similar in structure to the models familiar from model-theoretic semantics. Definites and Indefinites

37. Introduction Characterization of truth: a sentence S, or discourse D, with representation m is true in a model M if and only if M is compatible with m. (i.e. compatibility = existence of a proper embedding of m into M) The analysis deals with only a small number of linguistic problems . because of 2 central concerns: (a) study of the anaphoric behaviour of personal pronouns (b) formulation of a plausible account of the truth conditions of so called donkey sentences Definites and Indefinites

38. Introduction The Donkey Pedro (1) If Pedro owns a donkey he beats it. (2) Every farmer who owns a donkey beats it. Definites and Indefinites

39. Introduction What the solution should provide: (i) a general account of the conditional (ii) a general account of the meaning of indefinite descriptions (iii) a general account of pronominal anaphora Definites and Indefinites

40. Introduction The three main parts of the theory: 1. A generative syntax for the mentioned fragment of English 2. A set of rules which from the syntactic analysis of a sentence, or sequence of sentences, derives one of a small finite set of possible non-equivalent representations 3. A definition of what it is for a map from the universe of a representation into that of a model to be a proper embedding, and, with that a definition of truth Definites and Indefinites

41. Hans KampDiscourse Representation Theory • discourse representations (DR’s) • basics • indefinites • truth • handling conditionals and universals • discourse representation structures (DRS’s) • features of the theory Definites and Indefinites

42. x y Pedro owns Chiquita x = Pedro y = Chiquita x owns y Discourse Representations (DR’s) universe of the DR (discourse referents) DR conditions • reducible • irreducible Definites and Indefinites

43. x y Pedro owns Chiquita x = Pedro y = Chiquita x owns y Forming DR’s • rules that operate on syntactic structure of sentences • e.g. CR.PN (construction rule for proper names): • introduce new discourse referent • identify this with proper name • substitute discourse referent for proper name Definites and Indefinites

44. x y Pedro owns Chiquita x = Pedro y = Chiquita x owns y x y Pedro owns Chiquita x = Pedro y = Chiquita x owns y He beats her x beats her x beats y More sentences Pedro owns Chiquita. He beats her.  there are terms that introduce new discourse referents (proper nouns, indefinites), other just refer to existing ones (personal pronouns) Definites and Indefinites

45. x y Pedro owns a donkey x = Pedro x owns y Indefinites CR.ID: • introduce new discourse referent • state that this has the property of being an instance of the proper noun to which it refers • substitute discourse referent for indefinite term donkey(y) Definites and Indefinites

46. Model and Truth • we have a model M with universe UM and interpretation function FMwhich represents the world • UM: domain (of entities) • FM: assigns names to members of UM, indefinite terms to sets of members of UM and e.g. pairs of members of UM to transitive verbs • then a sentence is true (in M) iff we can find a proper mapping between the DR of that sentence and M Definites and Indefinites

47. x y Pedro owns a donkey x = Pedro x owns y Truth example “Pedro owns a donkey” is true in M iff: • there exist two members of UM such that: • one of them corresponds to FM(Pedro) • the other is a member of FM(donkey) • the pair of them belongs to FM (own) donkey(y) Definites and Indefinites

48. x y a farmer owns a donkey farmer(x) donkey(y) x owns y x y a farmer owns a donkey farmer(x) donkey(y) x owns y he beats it x beats it x beats y Conditionals / Universals If a farmer owns a donkey, he beats it. Every farmer who owns a donkey beats it. antecedent → consequent  Definites and Indefinites

49. Discourse Representation Structures = structured family of Discourse Representations Definites and Indefinites

50. x y a farmer owns a donkey farmer(x) donkey(y) x owns y x y a farmer owns a donkey farmer(x) donkey(y) x owns y he pets it x pets y DRS example Pedro is a farmer. If a farmer owns a donkey, he pets it. Chiquita is a donkey. Pedro is a farmer  Chiquita is a donkey Definites and Indefinites