Inga Schepers, Konrad Diwold, Sebastian Bitzer Seminar Introduction to Semantics University of Osnabrueck Definites and Indefinites An introduction to two theories with non-quantificational analysis’ of indefinites

Definites and Indefinites2 File Change Semantics and the Familiarity Theory of Definiteness Irene Heim

Definites and Indefinites3 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 Indefinites4 Karttunen’s Discourse Referents A definite NP has to pick out an 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 Indefinites5 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 Indefinites6 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 (F 0 ). As soon as 1a) is uttered, the listener puts two cards into the file and goes on to get the following file:

Definites and Indefinites7 F 1 :1 2 -is a woman-is a dog -was bitten by 2-bit 1 Next, 1b) gets uttered, which prompts the listener to update F 1 to F 2 : F 2 : 1 2 -is a woman-is a dog -was bitten by 2-bit 1 -hit 2-was hit by one

Definites and Indefinites8 F 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 Indefinites9 Model of Semantic Interpretation syntactic representation logical forms file change potential files truth conditions

Definites and Indefinites10 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. satisfies F 1 iff a 1 is a woman, a 2 is a dog, and a 2 bit a 1

Definites and Indefinites11 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 Indefinites12 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 Indefinites13 Let us look at the example from the beginning in a more formal way: Dom(F 1 ) = Dom(F 2 ) = {1,2} Sat(F 1 ) = { : a 1 is a woman, a 2 is a dog, and a 2 bit a 1 } Sat(F 2 ) = { : is element of Sat(F 1 ) and is element of Ext(“hit”) }

Definites and Indefinites14 In our example we focused on a particular logical form for the sentence “She hit it” namely “She 1 hit it 1 ”. But there are infinitely many others. e.g. (1) She 1 hit it 1. (2) She 3 hit it 7. (3) She 2 hit it 1. 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 Indefinites15 ( 2)Let F be a file, p an atomic proposition. Then p is appropriate with respect to F only if, for every NP i with index i that p contains: if NP i is definite, then i is element of Dom(F), and if NP i 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 Indefinites16 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(F 0 + [ NP1 a cat]) = { :b1 is element of Ext(“cat”)}. (2) Sat((F 0 + [ NP1 a cat]) + [ S e 1 arrived]) = { :b1 is element of Ext(“cat”) and b 1 is element of (“arrived”)}.

Definites and Indefinites17 Adverbs of Quantification David Lewis

Definites and Indefinites18 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 Indefinites19 No doubt they are quantifiers. but what do they quantify over ? ? ? ? ?? ? ? ? ? ? ? ?

Definites and Indefinites20 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 Indefinites21 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 Indefinites22 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 Indefinites23 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 Indefinites24 So far no useful solutions

Definites and Indefinites25 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 Indefinites26 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 Indefinites27 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 Indefinites28 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 Indefinites29 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 Indefinites30 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 Indefinites31 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 Indefinites32 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 Indefinites33 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 Indefinites34 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 Indefinites35 A theory of Truth and Semantic Representation Hans Kamp

Definites and Indefinites36 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 Indefinites37 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 Indefinites38 Introduction The DonkeyPedro (1) If Pedro owns a donkey he beats it. (2) Every farmer who owns a donkey beats it.

Definites and Indefinites39 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 Indefinites40 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 Indefinites41 Hans Kamp Discourse Representation Theory discourse representations (DR’s) –basics –indefinites –truth handling conditionals and universals discourse representation structures (DRS’s) features of the theory

Definites and Indefinites42 Discourse Representations (DR’s) xy Pedro owns Chiquita x = Pedro y = Chiquita x owns y universe of the DR (discourse referents) DR conditions reducible irreducible

Definites and Indefinites43 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 xy Pedro owns Chiquita x = Pedro y = Chiquita x owns y

Definites and Indefinites44 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) xy Pedro owns Chiquita x = Pedro y = Chiquita x owns y xy Pedro owns Chiquita x = Pedro y = Chiquita x owns y He beats her x beats her x beats y

Definites and Indefinites45 Indefinites CR.ID: –i–introduce new discourse referent –s–state that this has the property of being an instance of the proper noun to which it refers –s–substitute discourse referent for indefinite term xy Pedro owns a donkey x = Pedro x owns y donkey(y)

Definites and Indefinites46 Model and Truth we have a model M with universe U M and interpretation function F M which represents the world –U M : domain (of entities) –F M : assigns names to members of U M, indefinite terms to sets of members of U M and e.g. pairs of members of U M 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 Indefinites47 Truth example “Pedro owns a donkey” is true in M iff: there exist two members of U M such that: –one of them corresponds to F M (Pedro) –the other is a member of F M (donkey) –the pair of them belongs to F M (own) xy Pedro owns a donkey x = Pedro x owns y donkey(y)

Definites and Indefinites48 Conditionals / Universals If a farmer owns a donkey, he beats it. Every farmer who owns a donkey beats it. xy a farmer owns a donkey farmer(x) donkey(y) x owns y xy a farmer owns a donkey farmer(x) donkey(y) x owns y he beats it x beats it x beats y  antecedent → consequent

Definites and Indefinites49 Discourse Representation Structures = structured family of Discourse Representations

Definites and Indefinites50 DRS example xy a farmer owns a donkey farmer(x) donkey(y) x owns y xy a farmer owns a donkey farmer(x) donkey(y) x owns y he pets it x pets y  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 Indefinites51 xy a farmer owns a donkey farmer(x) donkey(y) x owns y xy a farmer owns a donkey farmer(x) donkey(y) x owns y he pets it x pets y  Pedro is a farmer Chiquita is a donkey DRS terminology principal DR (contains discourse as a whole) subordinate DR (to the conditional) superordinate DR (to the conditional)

Definites and Indefinites52 DRS remarks just discourse referents from superordinate DR’s or current DR can be accessed, but not from subordinate DR’s a discourse is true (in M ) iff there is a proper mapping from the principal DR into M

Definites and Indefinites53 Features of the theory theory handles quantificational adverbs and indefinites in completely different ways: –unselective quantifiers –non-quantificational analysis of indefinites  thereby provides solution for donkey sentences uniform treatment of third person pronouns

Definites and Indefinites54 References from Portner and Partee, Formal Semantics: The Essential Readings, 2002: –Irene Heim, On the Projection Problem for Presuppositions, 1983b –Irene Heim, File Change Semantics and the Familiarity Theory of Definiteness, 1983a –David Lewis, Adverbs of Quantification, 1975 –Hans Kamp, A Theory of Truth and Semantic Representation, 1981 Hans Kamp and Uwe Reyle, From Discourse to Logic, 1993