Introduction Phenomena Discourse Context Operator Context Conclusion References
A Translation from Logic to English withDynamic Semantics
Elizabeth Coppock
University of Texas at Austin and Cycorp, Inc.
Jozef Stefan InstituteMarch 18, 2010
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Outline
Introduction
Phenomena
Discourse Context
Operator Context
Conclusion
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Introduction Phenomena Discourse Context Operator Context Conclusion References
General program
Goal: To define and implement an algorithm fortranslating formulas of CycL (predicate logic) intoconcise, natural-sounding English, withquantificational expressions, proper names,indefinites, definite descriptions, and pronouns,wherever appropriate
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Referring and non-referring expressions
Translating logical formulas into natural language requiresgenerating both:
I referring expressions, e.g. Mary∼ constants or closed non-atomic terms
I non-referring expressions, e.g. no woman∼ variables
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Two separate fields in NLG
I Generating Referring Expressions
I Tactical Generation (or ‘Realization’)
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Generating Referring Expressions
I Task: Provide an appropriate means of referring to a givenobject in a domain.
I Example: multiple books, book in question on a uniquetable.
I the book on the table
I Only genuinely referring expressions
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Generating Referring Expressions
I Task: Provide an appropriate means of referring to a givenobject in a domain.
I Example: multiple books, book in question on a uniquetable.
I the book on the table
I Only genuinely referring expressions
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Generating Referring Expressions
I Task: Provide an appropriate means of referring to a givenobject in a domain.
I Example: multiple books, book in question on a uniquetable.
I the book on the table
I Only genuinely referring expressions
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Generating Referring Expressions
I Task: Provide an appropriate means of referring to a givenobject in a domain.
I Example: multiple books, book in question on a uniquetable.
I the book on the table
I Only genuinely referring expressions
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Generating “quantified” referring expressions
Systems for generating “quantified” referring expressions(Shaw and McKeown 2000; Varges and Van Deemter 2005):
I those women who have fewer than two children
I the people who work for exactly 2 employers
These refer to groups⇒ are referential
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Tactical generation
Based on formal grammatical theories, e.g.
I HPSG (Wilcock and Matsumoto 1998; Carroll et al. 1990;Copestake et al. 2005; Carroll and Oepen 2005)
I LFG (Wedekind and Kaplan 1996; Wedekind 1999; Kaplanand Wedekind 2000; Cahill and van Genabith 2006)
I CCG (Calder et al. 1989; Phillips 1993; White 2004)
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Quantificational input
From Pollard and Yoo (1998), implemented in Wilcock andMatsumoto (1998):
DET forall
RESTIND
INDEX 4
RESTR
QUANTS 〈〉
NUCLEUS
[
RELN student
INST 4
]
I But no representation of the discourse.
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How to combine strengths?
I Plop a GRE system onto a tactical generation system?I No: common constraints between bound & referential
anaphora
I Referring and non-referring expressions should be treatedwithin a unified framework.
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How to combine strengths?
I Plop a GRE system onto a tactical generation system?I No: common constraints between bound & referential
anaphora
I Referring and non-referring expressions should be treatedwithin a unified framework.
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How to combine strengths?
I Plop a GRE system onto a tactical generation system?I No: common constraints between bound & referential
anaphora
I Referring and non-referring expressions should be treatedwithin a unified framework.
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Dynamic Semantics
I e.g. Discourse Representation Theory (DRT; Kamp andReyle 1993) and File Change Semantics (Heim 1982)
I Captures the insight that referential and bound variableanaphora have certain commonalities
I Use ‘discourse referents’ (Karttunen 1976), which can beintroduced in the course of the discourse
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Dynamic Semantics
I e.g. Discourse Representation Theory (DRT; Kamp andReyle 1993) and File Change Semantics (Heim 1982)
I Captures the insight that referential and bound variableanaphora have certain commonalities
I Use ‘discourse referents’ (Karttunen 1976), which can beintroduced in the course of the discourse
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Dynamic Semantics
I e.g. Discourse Representation Theory (DRT; Kamp andReyle 1993) and File Change Semantics (Heim 1982)
I Captures the insight that referential and bound variableanaphora have certain commonalities
I Use ‘discourse referents’ (Karttunen 1976), which can beintroduced in the course of the discourse
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Karttunen’s discourse referents
I Karttunen (1976): “the appearance of an indefinite nounphrase establishes a discourse referent just in case it justifiesthe occurrence of a coreferential pronoun or a definitenoun phrase later in the text.”
I This definition allows the study of coreference to proceed“independently of any general theory of extralinguisticreference” (p. 367).
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Karttunen’s discourse referents
I Karttunen (1976): “the appearance of an indefinite nounphrase establishes a discourse referent just in case it justifiesthe occurrence of a coreferential pronoun or a definitenoun phrase later in the text.”
I This definition allows the study of coreference to proceed“independently of any general theory of extralinguisticreference” (p. 367).
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DRT Example (Top-down DRS construction)
S
NP
Det
a
N
linguist
VP
V
likes
NP
Mary
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DRT Example (Top-down DRS construction)
x
linguist′(x)&S
x VP
V
likes
NP
Mary
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DRT Example (Top-down DRS Construction)
x, m
linguist′(x) & Mary(m) & x likes m
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So start with Discourse Representation Structures?
∃x[linguist(x) ∧ likes(x,Mary)]
x, m
linguist′(x) & Mary(m) & x likes m
A linguist likes Mary
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So start with Discourse Representation Structures?
∃x[linguist(x) ∧ likes(x,Mary)]
x, m
linguist′(x) & Mary(m) & x likes m
A linguist likes Mary
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So start with Discourse Representation Structures?
∃x[linguist(x) ∧ likes(x,Mary)]
x, m
linguist′(x) & Mary(m) & x likes m
A linguist likes Mary
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A DRS is not a good starting point
I This strategy does not capture phenomena that reflectchanges to the discourse context as the discourse proceeds.
I If the input is a fully-formed DRS, then the discourserepresentation will remain fixed throughout the generationprocedure.
I The dynamic nature of the framework is not utilized undersuch an approach.
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A DRS is not a good starting point
I This strategy does not capture phenomena that reflectchanges to the discourse context as the discourse proceeds.
I If the input is a fully-formed DRS, then the discourserepresentation will remain fixed throughout the generationprocedure.
I The dynamic nature of the framework is not utilized undersuch an approach.
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A DRS is not a good starting point
I This strategy does not capture phenomena that reflectchanges to the discourse context as the discourse proceeds.
I If the input is a fully-formed DRS, then the discourserepresentation will remain fixed throughout the generationprocedure.
I The dynamic nature of the framework is not utilized undersuch an approach.
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Present framework
I Inspired by some of the ideas underlying DRT, including‘discourse referent’
I But: the discourse is built up as the sentence is generated.
I Dynamic in this sense.
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Present framework
I Inspired by some of the ideas underlying DRT, including‘discourse referent’
I But: the discourse is built up as the sentence is generated.
I Dynamic in this sense.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Present framework
I Inspired by some of the ideas underlying DRT, including‘discourse referent’
I But: the discourse is built up as the sentence is generated.
I Dynamic in this sense.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Outline
Introduction
PhenomenaDeterminer selectionLifespan limitations
Discourse Context
Operator Context
Conclusion
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Determiner selection
Direct translation
∀x[isa(x,Man)→ loves(x, x)]
For every x, if x is a man, then x loves x.
This is English, but we would like:
Every man loves himself.
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Determiner selection
A simple algorithm
∀ ∃| |
every some
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Determiner selection
The simple algorithm works in simple cases
∀x[loves(Mary, x)]
Mary loves everything.
∃x[loves(Mary, x)]
Mary loves something.
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Determiner selection
Exception: Donkey sentences
∀x∀y isa(x,Donkey)∧ isa(x,Farmer)∧ owns(x, y)→ beats(x, y)
If a farmer owns a donkey, then he beats it.
Not:
If every farmer owns every donkey, then he beats it.
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Determiner selection
Universally quantified variables under negation
∀x[isa(x,Donkey)→ ¬loves(Mary, x)]
Mary doesn’t love any donkey(s).
Mary loves no donkey(s).
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Determiner selection
No any in subject position
∀x[isa(x,Donkey)→ ¬loves(x,Mary)]
No donkeys love Mary.
Not:
*Any donkeys don’t love Mary.
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Determiner selection
Relative scope matters
¬∀x[loves(Mary, x)]
Mary doesn’t love everything.
∀x[¬loves(Mary, x)]
Mary doesn’t love anything.
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Determiner selection
Existentials indefinite
∃x[loves(Doug, x)]
Doug loves something.
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Determiner selection
Existentially bound variables and negation
∃x[¬loves(x,Mary)]
Someone doesn’t love Mary.
∃x[¬loves(Mary, x)]
Mary doesn’t love someone.
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Determiner selection
Existentially bound variables and negation, cont’d
¬∃x[loves(Mary, x)]
Mary doesn’t love anyone. / Mary loves noone.
¬∃x[loves(x,Mary)]
Noone loves Mary. / *Anyone doesn’t love Mary.
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Lifespan limitations
Everyone needs anaphora
Constants:
loves(Mary,Mary)
Mary loves herself.
And variables:
∀x¬loves(x, x)
No woman loves herself.
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Lifespan limitations
Short term referents
A normal referent survives for a while:
I found Mary’s cat and kept it. Then it ran away.
A short term referent can die abruptly (Heim 1983):
Everybody found a cat and kept it. *Then it ran away.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Lifespan limitations
Short term referents
A normal referent survives for a while:
I found Mary’s cat and kept it. Then it ran away.
A short term referent can die abruptly (Heim 1983):
Everybody found a cat and kept it. *Then it ran away.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Lifespan limitations
Short term referents
A normal referent survives for a while:
I found Mary’s cat and kept it. Then it ran away.
A short term referent can die abruptly (Heim 1983):
Everybody found a cat and kept it. *Then it ran away.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Lifespan limitations
Short term referents
A normal referent survives for a while:
I found Mary’s cat and kept it. Then it ran away.
A short term referent can die abruptly (Heim 1983):
Everybody found a cat and kept it. *Then it ran away.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Lifespan limitations
A better example?
Proper name antecedent:
Jane will give you her number. I know her.
Quantificational NP antecedent:
No self-respecting lady will give you her number. *I know her.
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Lifespan limitations
A better example?
Proper name antecedent:
Jane will give you her number. I know her.
Quantificational NP antecedent:
No self-respecting lady will give you her number. *I know her.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Lifespan limitations
A better example?
Proper name antecedent:
Jane will give you her number. I know her.
Quantificational NP antecedent:
No self-respecting lady will give you her number. *I know her.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Lifespan limitations
A better example?
Proper name antecedent:
Jane will give you her number. I know her.
Quantificational NP antecedent:
No self-respecting lady will give you her number. *I know her.
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Lifespan limitations
Different determiners, different lifespans
Referents introduced by indefinites last longer:
If a farmer owns
{
a donkey*every donkey
}
, then he beats it.
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Lifespan limitations
Our solution: Side effects
I We recursively define a generation function G(α), where αcan be any expression of the logic
I G depends not only on α, but also on the discourse contextD and the operator context O
I G can modify D and O
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Lifespan limitations
Our solution: Side effects
I We recursively define a generation function G(α), where αcan be any expression of the logic
I G depends not only on α, but also on the discourse contextD and the operator context O
I G can modify D and O
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Lifespan limitations
Our solution: Side effects
I We recursively define a generation function G(α), where αcan be any expression of the logic
I G depends not only on α, but also on the discourse contextD and the operator context O
I G can modify D and O
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Outline
Introduction
Phenomena
Discourse ContextDefinitionResults
Operator Context
Conclusion
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Definition
Discourse context
A discourse context D contains a set of discourse referents,composed of:
I a logical expression α, either an individual-denotingclosed term or a variable ranging over individuals.
I index features: person, number and genderI These will not be shown.
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Definition
Aside: Letting discourse referents be constants
DRT treats all discourse referents as variables. Issues:
I Conversion to PL is complicated (Kamp and Reyle 1993):
x, y
Mary(x)dog(y)
owns(x, y)
∃xy[x = Mary ∧ dog(y) ∧ owns(x, y)]
I Allowing constants to be discourse referents eliminates theneed for ‘external anchoring’ (Muskens 1996).
I Allowing constant discourse referents is natural from NLgeneration perspective.
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Definition
Aside: Letting discourse referents be constants
DRT treats all discourse referents as variables. Issues:
I Conversion to PL is complicated (Kamp and Reyle 1993):
x, y
Mary(x)dog(y)
owns(x, y)
∃xy[x = Mary ∧ dog(y) ∧ owns(x, y)]
I Allowing constants to be discourse referents eliminates theneed for ‘external anchoring’ (Muskens 1996).
I Allowing constant discourse referents is natural from NLgeneration perspective.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Aside: Letting discourse referents be constants
DRT treats all discourse referents as variables. Issues:
I Conversion to PL is complicated (Kamp and Reyle 1993):
x, y
Mary(x)dog(y)
owns(x, y)
∃xy[x = Mary ∧ dog(y) ∧ owns(x, y)]
I Allowing constants to be discourse referents eliminates theneed for ‘external anchoring’ (Muskens 1996).
I Allowing constant discourse referents is natural from NLgeneration perspective.
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Definition
What makes the semantics dynamic
If α is an individual-denoting constant or a variable rangingover individuals, then G(α) adds α to D.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example
[
PHON “Mary loves herself”
SEM loves(Mary,Mary)
]
[
PHON “Mary”
SEM Mary
]
[
PHON “loves”
SEM loves
] [
PHON “herself”
SEM Mary
]
D: {Mary}
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Definition
Example
[
PHON “Mary loves herself”
SEM loves(Mary,Mary)
]
[
PHON “Mary”
SEM Mary
]
[
PHON “loves”
SEM loves
] [
PHON “herself”
SEM Mary
]
D: {Mary}
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Definition
Example
[
PHON “Mary loves herself”
SEM loves(Mary,Mary)
]
[
PHON “Mary”
SEM Mary
]
[
PHON “loves”
SEM loves
] [
PHON “herself”
SEM Mary
]
D: {Mary}
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example
[
PHON “Mary loves herself”
SEM loves(Mary,Mary)
]
[
PHON “Mary”
SEM Mary
]
[
PHON “loves”
SEM loves
] [
PHON “herself”
SEM Mary
]
D: {Mary}
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example
[
PHON “Mary loves herself”
SEM loves(Mary,Mary)
]
[
PHON “Mary”
SEM Mary
]
[
PHON “loves”
SEM loves
] [
PHON “herself”
SEM Mary
]
D: {Mary}
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Definition
Example
[
PHON “Mary loves herself”
SEM loves(Mary,Mary)
]
[
PHON “Mary”
SEM Mary
]
[
PHON “loves”
SEM loves
] [
PHON “herself”
SEM Mary
]
D: {Mary}
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Definition
By the way: Generation templates
I Argument linking is accomplished via generation templates(genTemplate)
I e.g. likes: transitive sentence in whichI subject is the realization of the first argument,I the verb is a form of like that agrees with the subjectI the object is a realization of the second argument.
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Definition
Discourse referents corresponding to variables
[
PHON “Everything likes itself”
SEM ∀x likes(x, x)
]
[
PHON “Everything”
SEM x
]
[
PHON “likes”
SEM likes
] [
PHON “itself”
SEM x
]
D: {x}
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Discourse referents corresponding to variables
[
PHON “Everything likes itself”
SEM ∀x likes(x, x)
]
[
PHON “Everything”
SEM x
]
[
PHON “likes”
SEM likes
] [
PHON “itself”
SEM x
]
D: {x}
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Definition
Discourse referents corresponding to variables
[
PHON “Everything likes itself”
SEM ∀x likes(x, x)
]
[
PHON “Everything”
SEM x
]
[
PHON “likes”
SEM likes
] [
PHON “itself”
SEM x
]
D: {x}
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Discourse referents corresponding to variables
[
PHON “Everything likes itself”
SEM ∀x likes(x, x)
]
[
PHON “Everything”
SEM x
]
[
PHON “likes”
SEM likes
] [
PHON “itself”
SEM x
]
D: {x}
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Discourse referents corresponding to variables
[
PHON “Everything likes itself”
SEM ∀x likes(x, x)
]
[
PHON “Everything”
SEM x
]
[
PHON “likes”
SEM likes
] [
PHON “itself”
SEM x
]
D: {x}
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Discourse referents corresponding to variables
[
PHON “Everything likes itself”
SEM ∀x likes(x, x)
]
[
PHON “Everything”
SEM x
]
[
PHON “likes”
SEM likes
] [
PHON “itself”
SEM x
]
D: {x}
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Definition
Lifespan limitations
If α is a quantificational sentence binding a variable ξ, then ξmust be removed from D after computing G(α).
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Lifespan limitations
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves everything
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Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Suppose we did not remove x from D...
D: {Doug, x,Mary}
∀x¬[loves(Doug, x)] ∧ ∀x[loves(Mary, x)]
Doug loves nothing and Mary loves it← bad!
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Returning to Heim’s cat example
∀x∃y[found(x, y) ∧ kept(x, y)]
Everybody found a cat and kept iti.
Now, x and y are removed from the discourse context.
Iti ran away.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Returning to Heim’s cat example
∀x∃y[found(x, y) ∧ kept(x, y)]
Everybody found a cat and kept iti.
Now, x and y are removed from the discourse context.
Iti ran away.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Returning to Heim’s cat example
∀x∃y[found(x, y) ∧ kept(x, y)]
Everybody found a cat and kept iti.
Now, x and y are removed from the discourse context.
Iti ran away.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Results
Returning to Heim’s cat example
∀x∃y[found(x, y) ∧ kept(x, y)]
Everybody found a cat and kept iti.
Now, x and y are removed from the discourse context.
Iti ran away. ← impossible
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Outline
Introduction
Phenomena
Discourse Context
Operator ContextDefinitionExamples
Conclusion
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Operator Context: Definition
We define an operator context O as a tuple 〈V,S,n〉where:
I V is a set of variable type entries
I S is a stack of logical symbols 〈α1 . . . αn〉
I n is an integer representing the number of negationsremaining to be expressed.
A variable type entry v = 〈α, θ, τ〉, where:
I α is a variable over individuals,
I θ is a quantifier symbol
I τ is a type
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Operator Context: Definition
We define an operator context O as a tuple 〈V,S,n〉where:
I V is a set of variable type entries
I S is a stack of logical symbols 〈α1 . . . αn〉
I n is an integer representing the number of negationsremaining to be expressed.
A variable type entry v = 〈α, θ, τ〉, where:
I α is a variable over individuals,
I θ is a quantifier symbol
I τ is a type
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Clausal skeletons
∀x∀y isa(x,Man)∧ isa(y,Donkey)∧ owns(x, y)→ loves(x, y)
Clausal skeleton:
owns(x, y) → loves(x, y)
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Variable typing clauses
I isa formulas are variable typing clauses
I The binary predicate isa relates an individual to acollection, and signifies that the individual is an instance ofthe collection.
I Variable typing clauses are removed, along with theuniversal quantifiers.
I The types are stored in the operator context.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Variable typing clauses
I isa formulas are variable typing clauses
I The binary predicate isa relates an individual to acollection, and signifies that the individual is an instance ofthe collection.
I Variable typing clauses are removed, along with theuniversal quantifiers.
I The types are stored in the operator context.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Variable typing clauses
I isa formulas are variable typing clauses
I The binary predicate isa relates an individual to acollection, and signifies that the individual is an instance ofthe collection.
I Variable typing clauses are removed, along with theuniversal quantifiers.
I The types are stored in the operator context.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Variable typing clauses
I isa formulas are variable typing clauses
I The binary predicate isa relates an individual to acollection, and signifies that the individual is an instance ofthe collection.
I Variable typing clauses are removed, along with theuniversal quantifiers.
I The types are stored in the operator context.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Constructing clausal skeletons
For an input formula ∀ξα:
I If α ∼ [ψ → φ]:I If ψ ∼ [isa(ξ, γ)]:σ = φ
v = 〈ξ, ∀, γ〉I Else if ψ ∼ [δ1 ∧ ... ∧ δn] where δi ∼ [isa(ξ, γ)]:σ = [δ1 ∧ ... ∧ δi−1 ∧ δi+1 ∧ ... ∧ δn]→ φ
v = 〈ξ, ∀, γ〉I Else:σ = α
v = 〈ξ, ∀,Thing〉
I Else:σ = α
v = 〈ξ,∀,Thing〉
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Constructing clausal skeletons
For a formula of the form ∃ξα:
I If α ∼ [δ1 ∧ ... ∧ δn] where δi ∼ [isa(ξ, γ)]:σ = [δ1 ∧ ... ∧ δi−1 ∧ δi+1 ∧ ... ∧ δn]v = 〈ξ,∃, γ〉
I Else:σ = α
v = 〈ξ,∃,Thing〉
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Procedure
I The variable type entry v is added to the set V of variabletype entries in the operator context O;
I G(σ) is computed;
I Then the operator context is restored to its previous state.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Procedure
I The variable type entry v is added to the set V of variabletype entries in the operator context O;
I G(σ) is computed;
I Then the operator context is restored to its previous state.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Procedure
I The variable type entry v is added to the set V of variabletype entries in the operator context O;
I G(σ) is computed;
I Then the operator context is restored to its previous state.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example: Donkey sentence
V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example: Donkey sentence
V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example: Donkey sentence
V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example: Eliminating the antecedent
V: {〈x,∀,Man〉}
isa(x,Man)→ loves(x,Mary)
Every man loves Mary.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example: Eliminating the antecedent
V: {〈x,∀,Man〉}
isa(x,Man)→ loves(x,Mary)
Every man loves Mary.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Example: Eliminating the antecedent
V: {〈x,∀,Man〉}
isa(x,Man)→ loves(x,Mary)
Every man loves Mary.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Negation stripping
I When α is of the form ¬φ, the clausal skeleton of α is φ.
I No variable type entries are produced in this case.
I But the counter representing the number of unexpressednegations, n, is incremented.
I And ¬ is pushed onto the operator stack.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Negation stripping
I When α is of the form ¬φ, the clausal skeleton of α is φ.
I No variable type entries are produced in this case.
I But the counter representing the number of unexpressednegations, n, is incremented.
I And ¬ is pushed onto the operator stack.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Negation stripping
I When α is of the form ¬φ, the clausal skeleton of α is φ.
I No variable type entries are produced in this case.
I But the counter representing the number of unexpressednegations, n, is incremented.
I And ¬ is pushed onto the operator stack.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Negation stripping
I When α is of the form ¬φ, the clausal skeleton of α is φ.
I No variable type entries are produced in this case.
I But the counter representing the number of unexpressednegations, n, is incremented.
I And ¬ is pushed onto the operator stack.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Updating the operator stack
I If α ∼ ∀ξφ, then push ξ onto S and pop it off after G(α).
I If α ∼ ¬φ then push ¬ onto S and pop it off after G(α).
I If α ∼ φ→ ψ then push→ onto S and pop it off after G(φ).
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Variable realization algorithm
Suppose 〈ξ, θ, τ〉 ∈ V.
I If ξ is in D, then realize it with a pronoun if its antecedentis sufficiently salient and the pronoun would not beambiguous.
I Otherwise, realize it with a determiner followed by a nounexpressing τ .
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Determiner selection algorithm: Computing π
First step in choosing a determiner: Compute π.
I If θ = ∀, is the variable is deeper on the stack than an NPIlicenser (→ or ¬)?
I If so, set π equal to the NPI licenser
I If θ = ∃, is there an NPI licenser is deeper than it?I If so, set π equal to the NPI licenser
If the variable has no NPI licenser, then π is null.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Determiner selection algorithm: Computing π
First step in choosing a determiner: Compute π.
I If θ = ∀, is the variable is deeper on the stack than an NPIlicenser (→ or ¬)?
I If so, set π equal to the NPI licenser
I If θ = ∃, is there an NPI licenser is deeper than it?I If so, set π equal to the NPI licenser
If the variable has no NPI licenser, then π is null.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Definition
Determiner selection algorithm
Given π,
I If ξ is in D, return that or the.
I If π is non-null:I If π = ¬ and n > 0, then return no and decrement n by one.I Otherwise, return any or a/an.*
I If θ = ∀, return every.
I Otherwise, return a/an.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: nothing
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary loves nothing
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 1π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: anything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈x,¬〉n: 0π : ¬
∀x¬[loves(Mary, x)]
Mary doesn’t love anything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 0π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 1π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 1π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 1π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 1π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 1π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 1π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 0π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 0π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: not ... everything
D: 〈Mary, x〉V: {〈x,∀,Thing〉}S: 〈¬, x〉n: 0π : ∅
¬[∀x loves(Mary, x)]
Mary doesn’t love everything
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→ 〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→ 〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→ 〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→ 〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→ 〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→ 〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→ 〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Example: Donkey sentence
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x, y,→〉n: 0π :→
∀x∀y[isa(x, Farmer) ∧ isa(y,Donkey) ∧ owns(x, y)→ beats(x, y)]
If a farmer owns a donkey, then he beats it.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
64 / 68
Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
64 / 68
Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
64 / 68
Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
64 / 68
Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
64 / 68
Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
64 / 68
Introduction Phenomena Discourse Context Operator Context Conclusion References
Examples
Interaction between determiners and lifespans
D: {x, y}V: {〈x,∀,Farmer〉, 〈y,∀,Donkey〉}S: 〈x,→ , y〉n: 0π : ∅
∀x[isa(x, Farmer) ∧ ∀y[isa(y,Donkey)→ owns(x, y)]]→ . . .
If a farmer owns every donkey, then . . .
Now y is not in D⇒ no anaphora to every donkey
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Outline
Introduction
Phenomena
Discourse Context
Operator Context
Conclusion
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Summary
I Translating predicate logic to English requires generatingreferring and non-referring expressions, and they shouldbe treated in in a unified framework
I Our solution uses a dynamically-updated discourse contextD and operator context O.
I D is used for referring and non-referring expressionsI O is used for introducing non-referring expressions
I Captures use of quantificational determiners, and enforceslifespan limitations on discourse referents.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Summary
I Translating predicate logic to English requires generatingreferring and non-referring expressions, and they shouldbe treated in in a unified framework
I Our solution uses a dynamically-updated discourse contextD and operator context O.
I D is used for referring and non-referring expressionsI O is used for introducing non-referring expressions
I Captures use of quantificational determiners, and enforceslifespan limitations on discourse referents.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Summary
I Translating predicate logic to English requires generatingreferring and non-referring expressions, and they shouldbe treated in in a unified framework
I Our solution uses a dynamically-updated discourse contextD and operator context O.
I D is used for referring and non-referring expressionsI O is used for introducing non-referring expressions
I Captures use of quantificational determiners, and enforceslifespan limitations on discourse referents.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Outlook
Could the generation perspective shed light on issues insemantics more generally?
NPI licensing. Noone loves me blocks *Anyone doesn’t love me.
Accessibility. In DRT: a structural relationship betweendiscourse referents within DRSs. Here: apotentially transient state that ends when thequantificational expression has been realized.
Presupposition. Uniqueness of pronouns and definitedescriptions follows from procedure, notrepresented declaratively.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
Thank you!
Thanks to David Beaver, Nicholas Asher, Cleo Condoravdi,Anders Schoubye, Lucas Champollion, and Elias Ponvert forfeedback. This work was partially supported under theDARPA Rapid Knowledge Formation program.
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Introduction Phenomena Discourse Context Operator Context Conclusion References
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