Transcript Folie 1 - uni-osnabrueck.de
Definites and Indefinites
An introduction to two theories with non-quantificational analysis’ of indefinites Inga Schepers, Konrad Diwold, Sebastian Bitzer Seminar Introduction to Semantics University of Osnabrueck 19.06.2003
File Change Semantics and the Familiarity Theory of Definiteness
Irene Heim 19.06.2003
Definites and Indefinites 2
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.
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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 19.06.2003
Definites and Indefinites 4
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) 19.06.2003
Definites and Indefinites 5
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: 19.06.2003
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F 1 : 1 -is a woman -was bitten by 2 2 -is a dog -bit 1 Next, 1b) gets uttered, which prompts the listener to update F 1 to F 2 : F 2 : 1 -is a woman -was bitten by 2 -hit 2 2 -is a dog -bit 1 -was hit by one 19.06.2003
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F 3 : 1 -is a woman -was bitten by 2 -hit 2 2 -is a dog 3 -is a fence -bit 1 -was jumped over -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.
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Model of Semantic Interpretation
syntactic representation 19.06.2003
logical forms files file change potential files truth conditions Definites and Indefinites 9
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 19.06.2003
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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 19.06.2003
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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)) 19.06.2003
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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”) } 19.06.2003
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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: 19.06.2003
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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 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) 19.06.2003
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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]) = {
(2) Sat((F 0 + [ NP1 a cat]) + [ S e 1 arrived]) = {:b1 is element of Ext(“cat”) and b 1 is element of (“arrived”)}.
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Adverbs of Quantification
David Lewis 19.06.2003
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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 19.06.2003
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?
?
?
?
?
?
No doubt they are quantifiers.
but what do they quantify over
?
?
?
?
?
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Definites and Indefinites ?
?
19
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.
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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 19.06.2003
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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.
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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.
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So far no useful solutions
Definites and Indefinites 24
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 19.06.2003
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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.
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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 sometimes.
and can show up as always 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.
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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) 19.06.2003
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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
and then is a man, if
y
is a donkey, and if
x
owns
y
,
x
beats
y
now 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) 19.06.2003
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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.
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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
usuall
y
are a man and a donkey and if beats
y
now and then.
x
owns
y, x
4.2) If
x
and
y
and then if
x
are a man and a donkey, usually
x
owns
y
beats
y
now 19.06.2003
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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.
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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
4.8) if
x
4.9) if
x
is a donkey … is a old, grey donkey … 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.
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Displaced restrictive terms
5.0
Sometimes if
y
then is a donkey, and if some man Sometimes if some man
x
owns
y
, a donkey,
x x
owns
y, x
beats
y
beats
y
now and now and then Often if
x
then Often if
x
is someone who owns
y
, and if
y
is someone who owns
y
is a donkey, , a donkey,
x
beats
y x
beats
y
now and now and then Often if
x
is someone
x
who owns
y
, a donkey, beats
y
now and then 19.06.2003
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A theory of Truth and Semantic Representation
Hans Kamp 19.06.2003
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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.
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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 19.06.2003
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The Donkey
Introduction
Pedro (1) If Pedro owns a donkey he beats it.
(2) Every farmer who owns a donkey beats it.
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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 19.06.2003
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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 19.06.2003
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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 19.06.2003
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Discourse Representations (DR’s)
x y Pedro owns Chiquita x = Pedro y = Chiquita x owns y universe of the DR (discourse referents) DR conditions • reducible • irreducible 19.06.2003
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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 19.06.2003
Definites and Indefinites x y Pedro owns Chiquita x = Pedro y = Chiquita x owns y 43
More sentences
Pedro owns Chiquita. He beats her.
x y x y Pedro owns Chiquita x = Pedro y = Chiquita x owns y Pedro owns Chiquita x = Pedro y = Chiquita x owns y He beats her x beats her x beats y there are terms that introduce new discourse referents (proper nouns, indefinites), other just refer to existing ones (personal pronouns) 19.06.2003
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Indefinites
x y Pedro owns a donkey x = Pedro donkey(y) x owns y 19.06.2003
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 Definites and Indefinites 45
Model and Truth
• we have a model M with universe U M interpretation function F M and 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 19.06.2003
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Truth example
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x y Pedro owns a donkey x = Pedro donkey(y) x owns y “Pedro owns a donkey” is true in M iff: • there exist two members of U M such that: – one of them corresponds to – the other is a member of F M F M (Pedro) (donkey) – the pair of them belongs to F M (own) Definites and Indefinites 47
Conditionals / Universals
If a farmer owns a donkey, he beats it.
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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 Definites and Indefinites 48
Discourse Representation Structures
= structured family of Discourse Representations 19.06.2003
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DRS example
Pedro is a farmer. If a farmer owns a donkey, he pets it. Chiquita is a donkey.
x y a farmer owns a donkey farmer(x) donkey(y) x owns y Pedro is a farmer x y a farmer owns a donkey farmer(x) donkey(y) x owns y he pets it x pets y Chiquita is a donkey 19.06.2003
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DRS terminology
principal DR (contains discourse as a whole) superordinate DR (to the conditional) 19.06.2003
x y a farmer owns a donkey farmer(x) donkey(y) x owns y Pedro is a farmer x y a farmer owns a donkey farmer(x) donkey(y) x owns y he pets it x pets y Chiquita is a donkey subordinate DR (to the conditional) Definites and Indefinites 51
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 19.06.2003
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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 19.06.2003
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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 19.06.2003
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