definites and indefinites

Inga Schepers, Konrad Diwold, Sebastian BitzerSeminar Introduction to SemanticsUniversity of Osnabrueck19.06.2003

Definites and Indefinites

An introduction to two theories with non-quantificational

analysis’ of indefinites

19.06.2003 Definites and Indefinites 2

File Change Semantics and the Familiarity Theory of Definiteness

Irene Heim


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.


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


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)


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:


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


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.


Model of Semantic Interpretation

syntactic representation

logical forms

file change potentialfiles files

truth conditions


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


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


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))


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”) }


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:


(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)


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”)}.


Adverbs of Quantification

David Lewis


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


No doubt they are quantifiers.

but what do they quantify over

?

?

?

?

??

?

?

?

?

?

??


First Guess: Quantifiers over Time

May seem plausible:Example with always:

always is a modifier that combines with a sentence Φ to makethe sentence Always Φ that is true iff the modified sentence Φis 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.


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 althoughsimultaneous

1.3)Riders on the Thirteenth Avenue line seldom find seats


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 hereInterpretation 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 hisdonkey is punctuated by beatings.

BUT: Beatings are not events.


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.


So far no useful solutions


Third Guess:Quantifiers over Cases

What can be said: Adverbs of quantification are quantifiersover 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


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.



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.



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)


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)


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.


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


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 multiplied4.4) 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.


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.


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 thenOften if x is someone x who owns y, a donkey, beats y now and then


A theory of Truth andSemantic Representation

Hans Kamp


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.


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


IntroductionThe Donkey Pedro

(1) If Pedro owns a donkey he beats it.(2) Every farmer who owns a donkey beats it.


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


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


Hans KampDiscourse Representation Theory

• discourse representations (DR’s)– basics– indefinites– truth

• handling conditionals and universals

• discourse representation structures (DRS’s)

• features of the theory


Discourse Representations (DR’s)

x y

Pedro owns Chiquita

x = Pedroy = Chiquita

x owns y

universe of the DR(discourse referents)

DR conditions• reducible• irreducible


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

x y

Pedro owns Chiquita


x owns 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)

x y

Pedro owns Chiquita


x owns y

x y

Pedro owns Chiquitax = Pedro

y = Chiquitax owns y

He beats herx beats herx beats 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

x y

Pedro owns a donkey

x = Pedro

x owns y

donkey(y)


Model and Truth

• we have a model M with universe UM and interpretation function FM which 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


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)

x y

Pedro owns a donkey

x = Pedro

x owns y

donkey(y)


Conditionals / Universals

If a farmer owns a donkey, he beats it.

Every farmer who owns a donkey beats it.

x y

a farmer owns a donkey

farmer(x)donkey(y)x owns y

x y

a farmer owns a donkeyfarmer(x)donkey(y)x owns y

he beats itx beats itx beats y

antecedent → consequent


Discourse Representation Structures

= structured family of Discourse Representations


DRS example

x y



x y

a farmer owns a donkeyfarmer(x)donkey(y)x owns yhe pets itx 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


x y



x y

a farmer owns a donkeyfarmer(x)donkey(y)x owns yhe pets itx pets y

Pedro is a farmer

Chiquita is a donkey

DRS terminologyprincipal DR (contains discourse as a whole)

subordinate DR (to the conditional)

superordinate DR (to the conditional)


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


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


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

definites and indefinites

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