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

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.

4
Karttunens 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

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)

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

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
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.
9
Model of Semantic Interpretation

• syntactic representation

logical forms
file change potential
files
files
truth conditions
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.
• lta1,a2gt satisfies F1 iff a1 is a woman, a2 is a
  dog,
• and a2 bit a1

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

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(Fp))

13
Let us look at the example from the beginning in
a more formal way Dom(F1) Dom(F2)
1,2 Sat(F1) lta1,a2gt a1 is a woman, a2 is
a dog, and a2 bit a1 Sat(F2) lta1,a2gt
lta1,a2gt is element of Sat(F1) and lta1,a2gt
is element of Ext(hit)
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
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(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)
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) ltb1gtb1 is element of
Ext(cat). (2) Sat((F0 NP1a cat) Se1
arrived) ltb1gtb1 is element of
Ext(cat) and b1 is element of
(arrived).
17
Adverbs of Quantification

• David Lewis

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

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?

• No doubt they are quantifiers.
• but what do they quantify over

?
?
?
?
?
?
?
?
?
?
?
?
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First Guess Quantifiers over Time

• May seem plausible
• Example with always
• always is a modifier that combines with a
  sentence F to make
• the sentence Always F that is true iff the
  modified sentence F
• 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.

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

22
Second GuessQuantifiers 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.

23
Second GuessQuantifiers 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 couldnt cope with
  that kind of sentence
• 2.2) Quadratic equations are always simple.

24
So far no useful solutions
25
Third GuessQuantifiers 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

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 didnt
  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.

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.

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)

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)

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.

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

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.

33
Displaced restrictive terms

• Supposing a canonical sentence with a restrictive
  if-clause of the form
• (4.6) if a is t ,
• where a is a variable and t 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
• t is called restrictive term when used so.
• We can delete the if-clause and place the
  restrictive term t in apposition to an occurrence
  of the variable a elsewhere in the sentence.

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

35
A theory of Truth andSemantic Representation

• Hans Kamp

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.

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

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

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

41
Hans KampDiscourse Representation Theory

• discourse representations (DRs)
• basics
• indefinites
• truth
• handling conditionals and universals
• discourse representation structures (DRSs)
• features of the theory

42
Discourse Representations (DRs)
universe of the DR (discourse referents)
DR conditions

• reducible
• irreducible

43
Forming DRs

• 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

44
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)

45
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)
46
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

47
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)
48
Conditionals / Universals

• If a farmer owns a donkey, he beats it.
• Every farmer who owns a donkey beats it.

antecedent ? consequent
?
49
Discourse Representation Structures

• structured family of Discourse Representations

50
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
51
DRS terminology
principal DR (contains discourse as a whole)
superordinate DR (to the conditional)
Pedro is a farmer
?
Chiquita is a donkey
subordinate DR (to the conditional)
52
DRS remarks

• just discourse referents from superordinate DRs
  or current DR can be accessed, but not from
  subordinate DRs
• a discourse is true (in M) iff there is a proper
  mapping from the principal DR into M

53
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

54
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