Deep Lexical Semantics or Commonsense Knowledge and Lexical Semantics 2' Framework

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Deep Lexical SemanticsorCommonsense Knowledge
and Lexical Semantics2. Framework
Jerry R. Hobbs Information Sciences
Institute University of Southern
California Marina del Rey, CA
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Where Are We?

• Introduction Core theories of commonsense
• knowledge and their relation to the lexicon
• Framework Logic and abduction
• Cognition and the cognitive lexicon
• Time and now
• Causality and modality
• Similarity and like

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Outline

• Review of logic
• Reification to stay in first-order logic
• LCC Question-answering
• What is abduction?
• Abduction as an Everywhere Adequate
• framework
• Weighted abduction, the form of axioms,
• and incremental changes to axioms

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Defeasible, First-Order Logic
1. Conjunction (additive effect of two
propositions) 2. Implication and Modus Ponens
(associations, triggering) 3. Recognition of
Obvious Contradictions (inhibitory links) 4.
Predicate-Argument Relations 5. Universal
Instantiation, Variable Binding
Distinct instances of same generalization. 6.
Defeasibility Rules of inference applied
correctly to good premises usually
yields good conclusions. One
proof/conclusion can be better than another.
(non-demonstrative)
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Propositional Logic
Propositional constants P, Q, R, ... Have
vaues of either True or False. Logical
connectives and or ?
not or equivalent, iff
lt--gt or ? or v
imply --gt or ? Defined by truth tables
Latin word for or is vel
Q T F P T T
F F F F
v Q T F P T T
T F T F
P T F F T
Material impication either P is false or Q is
true
Definitions of lt--gt and --gt P lt--gtQ
lt--gt P --gt Q Q --gt P P
--gt Q lt--gt P v Q
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Properties of Logical Connectives
Properties of logical connectives Modus
ponens P P--gtQ --gt Q and v are
associative and commutative P Q R
lt--gt P Q R P Q lt--gt Q
P P v Q v R lt--gt P v Q v R
P v Q lt--gt Q v P so we can
write P Q R ... and P v Q v R v ...
(What about P --gt Q --gt R lt-?-gt
P --gt Q --gt R?) Relating , v and
P Q lt--gt P v Q
P v Q lt--gt P Q P Q v
R lt--gt P Q v P R P v Q R
lt--gt P v Q P v R Double
negation P lt--gt P
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First-Order Logic
Propositional logic Dont look inside
propositions P, Q, R, ... First-order logic
Look inside propositions p(x,y), like(J,M), ...
Constants John1, Sam1, ..., Chair-46, ..., 0,
1, 2, ... Variables x, y, z, .... Predicate
symbols p, q, r, ..., like, hate, ... Function
symbols motherOf, sumOf, ... All the logical
connectives of propositional logic. Predicates
and functions apply to a fixed number of
arguments Predicates like(John1,Mary1),
hate(Mary1,George1), tall(Sue3), ...
Functions motherOf(Sam1) Mary1, sumOf(2,3)
5, ... In the expression 3 2 gt 4
function
predicate
Predicates applied to arguments are propositions
and yield True or False. Functions applied to
arguments yield entities in the domain.
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Quantifiers
Two different roles for variables Recall from
high-school algebra (x y)(x - y) x2
- y2 x2 -7x 12 0
universal statement (A x,y)(x y)(x - y)
x2 - y2
existential statement (E x)x2 -7x 12
0
Universal quantifier A or ? statement is
true for all values of variable Existential
quantifier E or ? statement is true for some
value of variable
In (A x)p(x) q(y) x is bound by the
quantifier y is not. Both are in the scope
of the quantifier. Well only use variables that
are bound by a quantifier. The quantifier tells
how the variable is being used.
Relation between A and E (A x) p(x)
lt--gt (E x)p(x) Negation can be
moved inside (A x) p(x) lt--gt (A y) p(y)
The variable doesnt matter
(A x)p(x) Q lt--gt (A x)p(x) Q No harm
scoping over what where no x in Q
doesnt involve the
variable
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Horn Clauses
Horn clause A clause with one positive
literal. p(x,y) v q(x) v r(x,y) is
equivalent to p(x,y) q(x) --gt r(x,y)
procedure name
procedure body
The key idea in Prolog
Implicative normal form (A x,y)p1(x,y)
p2(x,y) ... --gt (E z)q1(x,z) q2(x,z)
... Useful for commonsense knowledge (A
x)car(x) intact(x) --gt (E z)engine(z)
in(z,x) Every intact car has an engine in it.
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Logical Theories and Rules of Inference
Logical theory The logic as we have
defined it so far A set of logical
expressions that are taken to be true
(axioms) Rules of inference Modus Ponens
From P, P --gt Q infer Q Universal
instantiation From (A x)p(x) infer
p(A) Theorems Expressions that can be
derived from the axioms and the rules
of inference.
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Models
What do the logical symbols mean? What do the
axioms mean?
A logical theory is used to describe some domain.
We assign an individual or entity in the domain
to each constant (the denotation of that
constant. To each unary predicate we assign a set
of entities in the domain, those entities
for which the predicate is true (the denotation
or extension of p). To each binary predicate we
assign a set of ordered pairs of entities,
etc. P true when P is not true. P Q true
when P is true and Q is true P v Q true when P
is true or when Q is true p(A) true when the
denotation of A is in the set assigned to p (A
x)p(x) true when for every assignment of x, x
is in the set assigned to p If all the axioms of
the logical theory are true, then the domain is a
model of the theory.
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Examples
x y z x y z u z x
v w w
Logical theory Predicate sum(x,y,z) (x
is the sum of y and z) Axiom 1 (A
x,y,z,w)(E u)sum(u,x,y) sum(w,u,z)
lt--gt
(E v)sum(v,y,z) sum(w,x,v)
(associativity) Some models addition of
numbers, multiplication of numbers
concatenation of strings
Add Axiom 2 (A x,y,w)sum(w,x,y) lt--gt
sum(w,y,x) (commutativity) Some
models addition of numbers, multiplication of
numbers
concatenation of strings In general, adding
axioms eliminates models.
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Some Uses of Models
Consistency A theory is consistent if you cant
conclude a contradiction. If a logical
theory has a model, it is consistent. Independenc
e Two axioms are independent if you cant prove
one from the other. To show two
axioms are independent, show that there is a
model in which one is true and the
other isnt true. Soundness All the theorems
of the logical theory are true in the
model. Completeness All the true statements in
the model are theorms in
the logical theory.
The logical theory should tell the whole truth
(complete) and nothing but the truth (sound)
Precision 100
Recall 100
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Extension vs. Intension
(not intention)
.... Clinton Bush
Extension president
W1 .... Clinton Bush W2 ....
Clinton Gore W3 ....
Clinton Bush Kerry
Intension president
Frees meaning of predicate from accidents of how
the world is
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Survival Logic for This Course
If your eyes start to glaze over from too many
logical formulas..... Read only the
predicates Fit them into an English
sentence in the most charitable
way possible.
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Outline

• Review of logic
• Reification to stay in first-order logic
• LCC Question-answering
• What is abduction?
• Abduction as an Everywhere Adequate
• framework
• Weighted abduction, the form of axioms,
• and incremental changes to axioms

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Back to Language
Logic is about representing information.
Language conveys information. Logic is a good
way to represent the information conveyed by
language.
A man builds a boat. (E x,y)man(x) build(x,y)
boat(y) A tall man builds a small boat. (E
x,y)tall(x) man(x) build(x,y) small(y)
boat(y)
Seems simple enough, but problems arise.
(e.g., the determiner a, the present tense,
tall/small for what) Two ways to deal with these
problems Complicate the logic.
Complicate our conceptualization of the
underlying domain.
Much computational semantics
Me
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Reifying Events
Events can be modified John ran slowly. Events
can be placed in space and time On Tuesday,
John ran in Chicago. Events can be causes and
effects John ran, because Sam was chasing him.

Because John ran, he was tired. Events can
be objects of propositional attitudes Sam
believes John ran. Events can be nominalized
Johns running tired him out. Events can be
referred to by pronouns John ran, and Sam saw
it. To represent these, we need some kind of
handle on the event. We need constants and
variables to be able to denote events. We need
to treat events as things -- reify events
(from Latin re(s) - thing)
Let e1 be Johns running. Then slow(e1)

believe(Sam,e1) onDay(e1, ...), in(e1,
Chicago) tiredOut(e1, John) cause(...,
e1), cause(e1, ...) see(Sam, e1)
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Representing Reifications
Why not this? slow( run(John) )
This evaluates to True or False Then slow would
describe not Johns running, but True or False
This is easily understood, but it takes us out of
logic.
e1 run(John) run(e1,John)
This means e1 is the event of Johns running
Ill use this when I need to run(John)
otherwise.
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Reifying Everything
Not just events, but states, conditions,
properties John fell because the floor was
slippery. cause(e1,e2)
fall(e2, j) slippery(e1, f) I will use the
word eventuality to describe all these
things -- events, states, conditions, etc.
Controversial
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Representing Case Relations
Jenny pushed the chair from the living room to
the dining room for Sam yesterday
Case
Agent
Theme
Source
Goal
Benefactor
Time
Could represent this like push(Jenny,
Chair1, LR, DR, Sam, 29Jun05, ...) Or like
push(e) Agent(Jenny,e) Theme(Chair1,e)
Source(LR,e) Goal(DR,e)
Benefactor(Sam,e) atTime(e, 29Jun05) Or like
push(e, Jenny, Chair1) from(e, LR) to(e,
DR) for(e, Sam)

yesterday(e, ...)
from complements
from adjuncts
Equivalence of these (A e,x,y)push(e,x,y) --gt
Agent(x,e) Theme(y,e)
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Space, Time, Tense, and Manner
tense
John ran. run(e,J) Past(e) John ran on
Tuesday. run(e,J) Past(e) onDay(e,d)
Tuesday(d) John ran in Chicago. run(e,J)
Past(e) in(e,Chicago) John ran slowly.
run(e,J) Past(e) slow(e) John ran
reluctantly. run(e,J) Past(e)
reluctant(J,e)
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Attributives
Some attributive adjectives have an implicit
comparison set or scale A small elephant
is bigger than a big mosquito. That
mosquito is big. mosquito(x) big(x, s)
The implicit comparison set or scale, which must
be determined from context
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Proper Names
Proper names Could treat them as
constants Springfield is the capital
of Illinois. gt capital(Springfield,
Illinois) But there are many Springfields
we could treat it as a predicate true
of any town named Springfield
capital(x,y) Springfield(x) Illinois(y)
Or we could treat the name as a string, related
to the entity by the predicate name
capital(x,y) name(Springfield,
x) name(Illinois, y)
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Indexicals
An indexical or deictic is a word or phrase that
requires knowledge of the situation of
utterance for its interpretation. I,
you, we, here, now, some uses of this,
that, ... The property of being I is being
the speaker of the current utterance Indexicals
require an argument for the utterance or the
speech situation. I(x,u) x is the speaker of
utterance u you(x,u) x is the intended hearer
of utterance u we(s,u) s is a set of people
containing the speaker of utterance u here(x,u)
x is the place of utterance u now(t,u) t is the
time of utterance u Chris said, I see you
now. gt say(Chris,u) content(e,u)
see(e,x,y) I(x,u) you(y,u)
atTime(e,t) now(t,u)
from the quotation marks
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Summary of Logical Form
The logical form of sentences is a flat
conjunction of existentially quantified
propositions John bought a new car. gt (E
j,e,c)John(j) buy(e,j,c) Past(e) new(c)
car(c) Knowledge is expressed as axioms in
implicative normal form A car has an engine.
gt (A x)car(x) --gt (E y) engine(y,x)
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Outline

• Review of logic
• Reification to stay in first-order logic
• LCC Question-answering
• What is abduction?
• Abduction as an Everywhere Adequate
• framework
• Weighted abduction, the form of axioms,
• and incremental changes to axioms

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Extended WordNet (XWN) and theLCC
Question-Answering System
Developed by Sanda Harabagiu, Dan Moldovan, and
Roxana Girju of Language Computer Corp,
Southern Methodist, U Texas Arlington, U
Texas Dallas Ongoing work since the mid
1990s. In TREC-2002 QA evaluation, LCC - 83
next two 58 and 54 everyone else under 40
Question
Match with large set of common patterns
full sentence parse
Question Processing
Document Retrieval
State of the art
Answer Reranking and Extraction
Answer
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LCC Components
Named entity recognizer Finite-state
patterns probabilistic decisions
part of speech (POS) tagging Syntactic parser
Probabilistic parser trained on typical
questions coreference resolution
heuristics Translation to logical form The
LF used in this class Theorem prover
Used for analyzing both the question and the
candidate answers
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Answer Extraction
Document retrieval component returns a ranked
list of subdocuments (passages within
documents) If too many, conjoin new query
terms (more key words from query) If too
few, disjoin new query terms (e.g.,
synonyms) Candidate answer reranking
Analyze the candidate subdocuments into their
logical form. Try to prove the logical form
of the question from the logical form
of the answer, using a large knowledge base.
The candidate answer with the best proof gets
ranked highest.
They say reranking candidate answers in this way
improved their score from 65 to 83, and
similar improvements in other evaluations.
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What Knowledge Base?Extended WordNet (XWN)
Disambiguate word senses in WordNet glosses
Automatic word sense disambiguation worked at 80
in Senseval Half of the glosses were
checked by hand So a word sense accuracy in
XWN of 90 Parse glosses and translate glosses
into logical form i.e., axioms Suicide is the
act of killing yourself. suicide(e1,x1) lt--gt
kill(e1,x1,x1) To kill is to cause to
die. kill(e1,x1,x2) lt--gt cause(e2,x1,e3)
die(e3,x2) Old is having lived for a
relatively long time or attained a specific
age. old(x6) lt--gt live(e2,x6,x2) for(e2,x1)
relatively(x1) long(x1)
time(x1) or(e5,e2,e3) attain(e3,x6,x2)
specific(x2) age(x2)
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The Search Space Problem
120,000 glosses --gt 120,000 axioms Theorem
proving would take forever. Lexical chains /
marker passing Try to find paths between
Answer Logical Form and Question Logical Form.
Ignore the arguments look for links between
predicates in XWN it becomes a graph
traversal problem (e.g., confuse buy, sell)
Observation All proofs use chains of
inference no longer than 4 steps Carry out
this marker passing only 4 levels out Q What
Spanish explorer discovered the Mississippi
River? Candidate A Spanish explorer Hernando
de Soto reached the Mississippi
River in 1536. Lexical chain
discover-v7 --GLOSS--gt reach-v1 Set of support
strategy Use only axioms that are on one of
these paths. 120,000 axioms gt several
hundred axioms
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Prove Question from Answer
Q How did Adolf Hitler die? QLF manner(e4)
Adolf(x10) Hitler(x11) nn(x12,x10,11)
die(e4,x12)
e4e5?
suicide is troponym of kill
suicide(e5,x12) --gt kill(e5,x12,x12)
manner(e5) Gloss of kill kill(e5,x12,x12)
lt--gt cause(e5,x12,e4) die(e4,x12) Gloss of
suicide suicide(e5,x12) lt--gt
kill(e5,x12,x12)
ALF it(x14) be(e1,x14,x2) Zhukov(x1)
s(x2,x1) soldier(x2)
plant(e2,x2,x3) Soviet(x3) flag(x3)
atop(e2,x4) Reichstag(x4) on(e2,x8)
May(x5) 1(x6) 1945(x7) nn(x8,x5,x6,x7)
day(x9) Adolf(x10) Hitler(x11)
nn(x12,x10,x11) commit(e3,x12,e5)
suicide(e5,x12) A It was Zhukovs soldiers
who planted a Soviet flag atop the Reichstag
on May 1, 1945, a day after Adolf Hitler
committed suicide.
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Relaxation (Assumptions)
Rarely or never can the entire Question Logical
Form be proved from the Answer Logical
Form gt We have to relax the Question
Logical Form Do tall men succeed? Logical
Form tall(e1,x1) x1x2 man(e2,x2)
x2x3 succeed(e3,x3) Remove these conjuncts
from what has to be proved, one by one, in
some order, and try to prove again. E.g., we
might find a mention of something tall and a
statement that men succeed. One limiting
case We find a mention of success. Penalize
proof for every relaxation, and pick the best
proof.
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Outline

• Review of logic
• Reification to stay in first-order logic
• LCC Question-answering
• What is abduction?
• Abduction as an Everywhere Adequate
• framework
• Weighted abduction, the form of axioms,
• and incremental changes to axioms

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What is Abduction?
Deduction p(a), (A x) p(x) --gt q(x) gt
q(a) Induction p(a), q(a) gt (A x) p(x)
--gt q(x) Abduction q(a), (A x) p(x) --gt
q(x) gt p(a)
Abduction Deduction
Assumptions Cost function on proofs
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(No Transcript)
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Interpreting the EnvironmentAbduction
Boat in Tree by Sea
Explain Entities in Environment
cause
Storm
Explain Relations in Environment
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Interpreting the EnvironmentPicking the Best
Explanation
boat in tree
tree down
crane
chopped down
storm
?
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Interpreting the EnvironmentPicking the Best
Explanation
boat in tree
tree down
in magazine
crane
chopped down
storm
ad agency
advertisement
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Interpretation as Abduction

• To Interpret a Situation Find the best
  explanation
• for the observables.
• Abduction Inference to the best explanation.
• Represent the observables as propositions.
• 2. Prove them, using the axioms in the knowledge
  base.
• 3. Allow assumptions in the proof, at a cost.
• 4. Pick the cheapest proof
• Shortest proof
• Fewest and most plausible assumptions
• Greatest redundancy
• Most salient axioms

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Interpreting Discourse

• An utterance presents "observable" propositions.
• To interpret an utterance, find the best
  explanation
• for the propositional content of the
  utterance.
• Represent the content as propositions (the
• logical form).
• 2. Prove them, using the axioms in the knowledge
  
• base.
• 3. Allow assumptions in the proof, at a cost.
• 4. Pick the cheapest proof
• Shortest proof
• Fewest and most plausible assumptions
• Greatest redundancy
• Most salient axioms

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Interpretation as Abduction
1. Represent the content as predications (the
logical form). 2. Prove them, using
the axioms in the knowledge base. 3.
Allow assumptions in the proof, at a cost. 4.
Pick the lowest cost proof.
Hearer
Speaker
MB
Utt
Uniform framework for syntax, semantics, and
pragmatics
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Abduction in LCCs System
Observable
Q General principle
P --gt Q Conclusion, assumption,
or explanation P
Inference to the best explanation
Abduction Try to prove Q the best you can
Make assumptions where you have to.
In the LCC QA system The question is the
observable Hitler died The XWN
glosses and troponyms are suicide --gt kill --gt
die the general principles The
answer is the explanation Hitler
committed suicide Relaxation is the assumptions
you have to make to get the proof to go
through.
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Outline

• Review of logic
• Reification to stay in first-order logic
• LCC Question-answering
• What is abduction?
• Abduction as an Everywhere Adequate
• framework
• Weighted abduction, the form of axioms,
• and incremental changes to axioms

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Definite Reference
John bought a new car. The engine is
already broken. LF . . . car(c) . . .
. . . engine(y,x) .
. . KB car(x) --gt engine(y,x) Definit
e Reference with Implicature John walked
into the room. The chandelier shone brightly.
LF . . . room(r) . . .
. . . chandelier(y) . . . KB
room(x) --gt light(y) in(y,x) light(y)
branching-fixtures(y) --gt chandelier(y)

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Lexical Ambiguity
The plane taxied to the terminal.
LF
plane(x) taxi(x,y) terminal(y)
KB
airplane(x) --gt plane(x)
move-on-ground(x,y) airplane(x) --gt taxi(x,y)
airport-terminal(y) --gt terminal(y)
airport(z) --gt airplane(x) airport-terminal(y)
wood-smoother(x) --gt plane(x)
ride-in-cab(x,y) person(x) --gt taxi(x,y)
computer-terminal(y) --gt terminal(y)
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Lexical Ambiguity
The plane taxied to the terminal.
LF
plane(x) taxi(x,y) terminal(y)
KB
airplane(x) --gt plane(x)
move-on-ground(x,y) airplane(x) --gt taxi(x,y)
airport-terminal(y) --gt terminal(y)
airport(z) --gt airplane(x) airport-terminal(y)
wood-smoother(x) --gt plane(x)
ride-in-cab(x,y) person(x) --gt taxi(x,y)
computer-terminal(y) --gt terminal(y)
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Syntax in the Abduction Framework
To interpret a text Prove that it is
composed of grammatical, interpretable
sentences (by proving the logical form
of the sentences) Allowing assumptions in
the proof, at a cost, Picking the lowest
cost proof.
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Syntax in the Abduction Framework
Grammar and Lexicon expressed as predicate
calculus axioms. Principal predicate Syn(w, e,
f, x, a, y, b,...)
category and feature structures of arguments
argument entities
category and feature structure of head eventuality
eventuality corresponding to head
string
Syn ("loves", e, V.Tnsd, x, N.Sing, y, N.Acc,...)
In this lecture, Syn(w, e, x, y)
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Composition Axioms
Form for S --gt NP VP Syn(w1, x,a, -,-,
-,-) Syn(w2, e,f, x,a, -,-) --gt
Syn(w1 w2, e,f, -, -, -, -) Form for VP --gt V
NP, PP --gt P NP, etc. Syn(w1, e,f, x,a,
y,b) Syn(w2, y,b, -,-, -,-) --gt
Syn(w1 w2, e,f, x,a, -,-)
About a dozen composition rules altogether,
closely following Pollard and Sag's HPSG
52
Lexical Axioms
At Frontier of Syntax and World
Knowledge during'(e,x,y) event(x)
time-period(y) --gt Syn ("during", e, P,
x, a, y, N.Acc)
pred-arg structure (incl word sense)
selectional constraints
category
subcategorization
spelling or phonology
One such axiom for each word sense or
subcategorization frame.
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Syntax A Parse
Relates string to entity
Explain Adjacency as Predicate-Argument
Syn("I flew to LA", e, -, -)
Link Syntax with World Knowledge
Composition Axioms
Syn("I", x, -, -)
Lexical Axiom
Syn("flew to LA", e, x, -)
I(x,u)
Syn("to LA", y, -, -)
Syn("flew", e, x, y)
Lexical Axiom
Lexical Axiom
LA(y)
past(e)
fly'(e,x,y)
(Then to interpret sentence, must prove logical
form abductively.)
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Alternation Axioms
Passive Syn (w, e, V.en, x, a, y, N.Acc)
--gt Syn (w, e, Pred, y, N.bCASE, -,
-) Metonymy Syn(w,e,x,y) rel(z,x)
--gt Syn(w,e,z,y) Syn(w,e,x,y)
rel(z,y) --gt Syn(w,e,x,z)
plays
Shakespeare
wrote
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Metonymy An Interpretive Move
Syn("read Shakespeare", e,x,-)
Syn("Shakespeare", y1, ...)
Syn("read", e, x, y1)
Metonymy
rel'(y2,y1)
Syn("read", e, x, y2)
Selectional Constraint
read'(e,x,y2) text(y2)
Coercion
Right Argument
play(y2) write(y1,y2) Shakespeare(y1)
Coerce "Shakespeare" into "plays of Shakespeare"
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Metonymy An Interpretive Move
Syn("read Shakespeare", e,x,-)
Find an author as Object
Syn("Shakespeare", y1, ...)
Syn("read", e, x, y1)
Find a text as Object
rel'(y2,y1)
Syn("read", e, x, y2)
read'(e,x,y2) text(y2)
Coercion
play(y2) write'(e3,y1,y2) Shakespeare(y1)
Coerce "Shakespeare" into "plays of Shakespeare"
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Lexical Decomposition
One Level below Lexical Frontier of Syntax and
World Knowledge kill'(e,x,y) --gt Syn
("kill", e, V, x, N, y, N) cause'(e,x,e1)
not'(e1,e2) alive'(e2,y) --gt kill'(e,x,y) open
2'(e,x,y) --gt Syn ("open", e, V, x, N, y,
N) cause'(e,x,e1) open1'(e2,y) --gt
open2'(e,x,y)
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Metonymy andLexical Decomposition
(Mark Gawron)
Syn("John opened the door again", e3, -, -)
Syn("John opened the door", e2, -, -)
Syn("again", e3, e2, -)
Metonymy
Syn("John", j, -, -)
Syn("again", e3, e1, -)
Syn("opened the door", e2, j, -)
rel(e1,e2)
John(j)
again'(e3,e1)
Syn("opened", e2, j, d)
Syn("the door", d, -, -)
Right Argument
door(d)
past(e2)
open2(e2,j,d)
Coercion
Lexical Decomposition
open1'(e1,d)
cause'(e2,j,e1)
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Interpreting Adjacent Sentences
Sentence-1
Sentence-2
Relation between
Event
Event
Possible Relations Cause Similarity
Background .....
Coherence Relations
60
Discourse Coherence
What information is conveyed by adjacency of
segments?
cause change of state figure-ground and
ground-figure similarity and contrast
Relation
Segment1 Segment2
Interpret each segment, and find the relation
between them.
R4 R3
R1 R2 S1 S2 S3 S4 S5
The Structure of Discourse
61
Formalizing the Tree Structureof Discourse
Syn(w,e,V,-,-,-,-) --gt Segment(w,e) Segment(w1,e1
) Segment(w2,e2) CoRel(e1,e2,e)
--gt Segment(w1 w2, e) Note
Syntactic composition rules are an instance
of this rule, where relation is
pred-arg. To interpret text, prove (? e)
Segment(text, e)
Summary
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Metaphor via Contrast
Mary is graceful.
John is an elephant.
CoRel(e1,e2)
Syn("John is an elephant",e2,-,-)
Contrast(e1,e2)
Syn(" is an elephant",e2,j,-)
Syn("John",j,-,-)
graceful'(e1,m)
Syn(" is",e2,j,-)
not'(e2,e4) graceful'(e4,j)
Syn("an elephant",e2,j,-)
person(m)
person(j)
Present(e2)
rel(e3,e2)
Mary(m)
Syn("an elephant",e3,j,-)
John(j)
elephant'(e3,j) --gt clumsy'(e2,j) imply(e3,e2)
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Metaphor via Contrast
Sentence's claim is John's clumsiness
Search for coherence forces metaphor reading
Mary is graceful.
John is an elephant.
CoRel(e1,e2)
Syn("John is an elephant",e2,-,-)
Contrast(e1,e2)
Syn(" is an elephant",e2,j,-)
Syn("John",j,-,-)
Coercion protects from contradiction
graceful'(e1,m)
Syn(" is",e2,j,-)
not'(e2,e4) graceful'(e4,j)
Syn("an elephant",e2,j,-)
person(m)
person(j)
Present(e2)
rel(e3,e2)
Mary(m)
Syn("an elephant",e3,j,-)
John(j)
This belief is source of metaphor
elephant'(e3,j) --gt clumsy'(e2,j) imply(e3,e2)
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The Speakers PlanA Context-Free Tautology
A Johnny certainly is misbehaving today. B
Boys will be boys.
A boy is a boy. X is a boy X is Y Y is
a boy. X Y Y
misbehaves If Y is a boy, then Y
misbehaves
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B's Plan
A believe B not responsible for J misbehaving A
believe J misbehaves necessarily A believe (X a
boy implies X misbehaves) B conveys to A that X
a boy implies X misbehaves B says to A that X
being a boy implies X being a boy B says to A
that X being a boy is X being a boy
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A Tautology in Context
A Johnny certainly is misbehaving today. B
Boys will be boys.
B says to A, "A boy is a boy."
X is a boy X is Y Y is a boy.
X Y Y misbehaves
If Y is a boy, then Y misbehaves
?
B not responsible for J's behavior
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Interpreting Intention
Explanation of a text Segment(w,e)
goal(i,c) Cog'(c,u,e) --gt
utter(i,u,w) If w is a coherent segment of
discourse conveying e, and if i has
the goal c of u "cognizing" e, then
(defeasibly) i will utter w to u. What is Cog
Declarative mood Cog believe
believe by virtue of utterance
entertain enter into conversational
record ... Interrogative mood
Cog u has goal that i knows e ...
Imperative mood Cog u has goal to do
e ...
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Interpreting Intention
Observable to be explained
utter(i,u,w)
Discourse Coherence
Segment(w,e)
goal(i,c)
Cog'(c,u,e)
Syn(w1,e1,-,-)
Syn(w2,e2,-,-)
CoRel(e1,e2,e)
Speaker's Plan Reasoning about goals and beliefs
Shared variables so mutual influence
Syntax
Logical Form
Reasoning with World Knowledge (Local
pragmatics, etc.)
THE LOCUS OF DEEP LEXICAL SEMANTICS
69
Outline

• Review of logic
• Reification to stay in first-order logic
• LCC Question-answering
• What is abduction?
• Abduction as an Everywhere Adequate
• framework
• Weighted abduction, the form of axioms,
• and incremental changes to axioms

70
Factors in Cost of Interpretations
What makes an interpretation good? 1. Salience
of Facts and Axioms Used in Proof 2. Size of
Proof 3. Number and Plausibility of
Assumptions 4. Use of Redundant Information in
Proofs
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Weighted Abduction
(Stickel, 1988) 1. Goal expressions are
assumable at cost (depending on utility
of explaining them). turpentine(x)3
nn(x,y)20 jar(y)10 2. Assumability costs
can be passed back. P1w1
P2w2 ---gt Q If Q costs c, then Pi
costs wi c. Informativity vs.
Reliability Trade-off 3. Factoring Goal
expressions can be unified, with minimum cost.
p(x1) p(x2) gt p(x)
Helps minimize size of proofs

72
Weighted Abduction
P1w1 P2w2 ---gt Q
If w1 w2 lt 1, more specific interpretations
are favored. If w1 w2 gt 1, less specific
interpretations are favored. But in
P1.6 P2.6 ---gt Q if
P1 is proved, it is cheaper to assume P2 than Q.
P1 provides evidence for Q.
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Weighted Abduction
Factoring can also override less specific
abduction Axioms P1.6 P2.6 ---gt Q1,
P2.6 P3.6 ---gt Q2 Goals Q110
Q210 Proof Q1
Q2 P1 P2 P2
P3 P1 P2
P3 Cost of assuming Q1 Q2 20 Cost
of assuming P1 P2 P3 18
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Range of Interpretations
most reliable
I went to Boston
optimum
I flew to Boston
Reliability
I flew to Boston on United
most informative
Informativity
75
Nonmonotonicity or DefeasibilityEtcetera
Propositions
bird(x)w1 etc1(x)w2 --gt fly(x)
You can never prove this, but you can assume
it for a cost. This may yield lowest cost
interpretation.
mammal(x)w3 etc2(x)w4 lt--gt elephant(x)
genus
differentiae
species
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The Form of Axioms
Implicative relation between p and q (A
x,y) p(x,y) --gt (E z) q(x,z) Add
eventualities (A x,y,e1) p(e1,x,y) --gt (E
z,e2) q(e2,x,z) Make rule part of explicit
knowledge (A x,y,e1) p(e1,x,y) --gt (E
z,e2) q(e2,x,z) imply(e1,e2) Make the rule
defeasible (A x,y,e1) p(e1,x,y)u
etc1(e1,x,y)v --gt (E z,e2) q(e2,x,z)
imply(e1,e2) Make the rule defeasibly
biconditional (A x,y,e1) p(e1,x,y)u1
etc1(e1,x,y)v1 --gt (E z,e2) q(e2,x,z)
imply(e1,e2) (A x,z,e2) q(e2,x,z)u2
etc2(e2,x,y)v2 --gt (E y,e1) p(e1,x,y)
imprel(e2,e1) The general form for expressing
associations between concepts.

77
What the Numbers MeanProbability of Occurrence
in Interpretation
Space of events Occurrences of propositions in
best proofs ( correct interpretations) for
all texts in corpus. P1w1 P2w2 ---gt Q
wi should vary with Pr(Q Pi). P1w1 ---gt
Q P2w2 ---gt Q wi should vary inversely
with Pr (Pi Q), .
with Pr ( P1 . . . Pk Q) .
anchored at 1. . Pkwk ---gt
Q Cost on goal expressions Utility of finding
more specific
interpretation.
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Incremental Changes to Axioms
(Learning, Development, Evolution)
1. Increase Arity of Predicates p(x)
gt p(x,y) mother(x) gt
mother(x,y) 2. Introduce new predicate p1 as
specialization of old predicate p
p1(x) --gt p(x) beagle(x)
--gt dog(x) 3. Add proposition to antecedent of
axiom p1(x) --gt q(x) gt p1(x)
p2(x) --gt q(x) seat(x) --gt chair(x)
gt seat(x) back(y,x) --gt chair(x) 4. Add
proposition to consequent of axiom
p(x) --gt q1(x) gt p(x) --gt q1(x)
q2(x) snow(x) --gt white(x) gt
snow(x) --gt white(x) cold(x)
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Incremental Changes to Axioms
2 3. Specialize predicates in antecedent
p(x) --gt q(x) gt p1(x) --gt q(x)
where
p1(x) --gt p(x) dog(x) --gt
floppy-ears(x) gt beagle(x) --gt
floppy-ears(x) 2 4. Specialize predicates in
consequent p(x) --gt q(x) gt p(x)
--gt q1(x)
where q1(x) --gt q(x) rabbit(x)
--gt mammal(x) gt rabbit(x) --gt rodent(x)
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Radial Categories
Word senses radiate via these incremental changes.
have a predication John had a drink.
p'(e,x) --gt have1(x,e)
have a small clause John had the pizza
delivered. p'(e,y) r(x,e) --gt have4(x,e)
have a future action John has yet to
call. future'(e1,e2) p'(e1,x) --gt
have2(x,e1) to'(e1,e2)
have an obligation John has to call.
oblig'(e1,e2) p'(e1,x) --gt have3(x,e1)
to'(e1,e2)
oblig'(e1,e2) --gt future'(e1,e2)
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Whats Next?

• Introduction Core theories of commonsense
• knowledge and their relation to the lexicon
• Framework Logic and abduction
• Cognition and the cognitive lexicon
• Time and now
• Causality and modality
• Similarity and like