CS 544: Lecture 3.4 Interpretation as Abduction and Local Pragmatics

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CS 544 Lecture 3.4Interpretation as
Abductionand Local Pragmatics

• Jerry R. Hobbs
• USC/ISI
• Marina del Rey, CA

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Logical Form
The logical form of a sentence (or text) is
an existentially quantified conjunction of
positive ground literals. (Existential
quantification is over a Platonic
universe of possible individuals, including
eventualities and typical elements.)
John didn't work again. gt (E j, e1, e2,
e3, e4, e5) Rexists(e5) again'(e5,e3)
not'(e3,e2) past'(e2,e4)
work'(e4,j) John'(e1,j) OR again(e3)
not'(e3,e2) past'(e2,e4) work'(e4,j) John(j)
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Outline
Abduction Solutions to Local Pragmatics
Problems using Abduction How Weighted
Abduction Works Some Systems Using Abduction
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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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Interpreting the Environment
observable-1 observable-2
observable-3
underlying
underlying
cause
cause
In Abduction,
deeper
best explanation
can be variable depth.
underlying
cause
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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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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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Cognitive Benefit
Knowledge of causal and implicational structure
of current situation
Ability to manipulate causal and implicational
structure of situation to achieve goals
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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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Factors in Cost
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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Knowledge Base / Belief System
Expressed as large collection of (defeasible)
axioms of form (? x,z) p1(x) p2(x,z) --gt
(? y) q1(y,x) q2(y) e.g., jar(y) --gt
container(y,x) fluid(x) (A jar
is a container for fluid) car(x) --gt
engine(y,x) (Cars have engines)
fly'(e1,x,y) --gt move-fast'(e,x,y)
imply(e1,e) (Flying implies moving
fast)
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Nonmonotonicity or Defeasibility
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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Outline
Abduction Solutions to Local Pragmatics
Problems using Abduction How Weighted
Abduction Works Some Systems Using Abduction
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Example
The Boston office called. Local Pragmatics
Problems illustrated 1. Definite Reference
What does the Boston office refer
to? 2. Interpreting compound nominals What is
the implicit relation between Boston
and office? 3. Metonymy Coerce from the
Boston office to someone at the
Boston office.
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The Example Interpreted
The Boston office called. LF
call'(e,x) person(x) rel(x,y)
office(y) Boston(z)

nn(z,y) KB person(J)
work-for(J,O), office(O)
work-for(x,y) --gt rel(x,y) in(O,B),
Boston(B) in(y,z) --gt nn(z,y)
New Information
Definite Reference
Metonymy
Compound Nominal
Local Pragmatics problems solved as a
by-product
Syntax Parse Tree Interpretation
Proof Graph
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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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Interpreting Compound Nominals
turpentine jar
Adjacency to be explained
turpentine(x)
jar(y)
nn(x,y)
fluid(x) container(y,x)
Proof is explanation of adjacency
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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
John wanted a loan. He went to
the bank. LF . . . loan(l) . . .
. . . bank(y) . . . KB loan(x)
--gt financial-institution(y)
issue(y,x) financial-institution
(y) etc4(y) --gt bank1(y)

bank1(y) --gt bank(y) river(z) --gt bank2(y)
borders(y,z) bank2(y) --gt bank(y)
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Metonymy as Part of Syntax
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'(e3,y1,y2) Shakespeare(y1)
Coerce "Shakespeare" into "plays of Shakespeare"
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Metonymy as Part of Syntax
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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Metonymy after Syntax
read'(e,x,y2) text(e1,y2) rel(e2,y2,y1)
Shakespeare(e3,y1)
rel(e2 y2,y1)
Selectional Constraint
read'(e,x,y2) text(e1 y2)
Coercion
Right Argument
play(e4,y2) write'(e3,y1,y2) Shakespeare(e3
y1)
Coerce "Shakespeare" into "plays of Shakespeare"
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Pragmatic Loosening as Coercion of Eventualities
Syn("flew to USC", e,x,-)
Syn("to USC", y, ...)
Syn("flew", e, x, y)
USC(y)
rel(e1,e)
Syn("flew", e1, x, y)
Coercion
past(e)
fly'(e1,x,y) --gt move-fast'(e,x,y) imply(e1,e)
"Figurative" predicate coerced into
inferentially related predicate.
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Pragmatic Loosening as Coercion of Eventualities
past(e) fly'(e1,x,y) rel(e1,e) to(e2,e1,y)
USC(y)
USC(y)
rel(e1,e)
Coercion
past(e)
fly'(e1,x,y) --gt move-fast'(e,x,y) imply(e1,e)
"Figurative" predicate coerced into
inferentially related predicate.
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Pronoun Resolution
The plain was reduced by erosion to its
present level. LF reduce'(e1,p,l) plain(p)
erode'(e2,x) present(e3) level'(e3,l,y) KB
To decrease on a vertical scale is to reduce
decrease(p,l,s) vertical(s)
etc1(p,l,s) --gt reduce'(e,p,l) A flat
landform is a plain landform(p)
flat(p) etc2(p) --gt plain(p) If a
flat thing Y is at a point L on a vertical scale,
then L is the level of Y
at'(e,y,l) on(l,s) vertical(s) flat(y)
etc3(e,y,l,s) ---gt
level'(e,l,y) One way for a landform to
decrease on the altitude scale is to erode
decrease'(x,l,s) landform(x)
altitude(s) etc4(x,l,s)
---gt erode'(e,x) One kind of vertical
scale is the altitude scale
vertical(s) etc5(s) --gt altitude(s)
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Pronoun Resolution
The plain was reduced by erosion to
its present level. KB decrease(p,l,s)
vertical(s) etc1(p,l,s) --gt reduce'(e,p,l)
landform(p) flat(p) etc2(p) --gt
plain(p) at'(e,y,l) on(l,s)
vertical(s) flat(y) etc3(e,y,l,s)
---gt level'(e,l,y) decrease'(x,l,s)
landform(x) altitude(s) etc4(x,l,s)
---gt erode'(e,x) vertical(s)
etc5(s) --gt altitude(s) Therefore, y (it ) x
p (the plain )
LF reduce(e1,p,l) plain(p) erode(e2,x)
present(e3) level(e3,l,y)
yp
xp
xp
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Schema Recognition and Matching
A bomb exploded at . . .
The FMLN claimed responsibility for . . .
Schema Axiom bomb-situation(e1,b, . .
. , g, e2, . . . ) ---gt bomb(b)
explode'(e1,b) . . .
terrorist-group(g)
responsible'(e2,g,e1) . . . Recognizing
schema yields minimal interpretation.
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Outline
Abduction Solutions to Local Pragmatics
Problems using Abduction How Weighted
Abduction Works Some Systems Using Abduction
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Factors in Most Economical Proof
Shortest proof Fewest and most plausible
assumptions Most salient axioms Greatest
redundancy
Language has a huge amount of implicit
redundancy. Recognizing redundancies yields more
propositions proved for fewer assumptions
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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

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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 Dallas
optimum
I flew to Dallas
Reliability
I flew to Dallas on Southwest
most informative
Informativity
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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.

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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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What the Numbers MeanFinding Proofs
0 P0 --gt Q Literal freely
assumable. e.g., P S0 --gt Q S is
side-effect. 1 P1 --gt Q No
added cost to using axiom. , d ltlt 1, n
number of literals in antecedent P1.6
P2.6 --gt Q Small added cost for
using axiom, favors not
backchaining unless partial proof or
redundancy. ????P? --gt Q Must
prove.
1d n
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Outline
Abduction Solutions to Local Pragmatics
Problems using Abduction How Weighted
Abduction Works Some Systems Using Abduction
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AQUAINT-I Question-Answeringfrom Multiple
Sources
Show me the region 100 km north of the capital of
Afghanistan.
Question Decomposition via Logical Rules
What is the capital of Afghanistan?
What is the lat/long 100 km north?
Show that lat/long
What is the lat/long of Kabul?
Terravision
CIA Fact Book
Alexandrian Digital Library Gazetteer
Geographical Formula
Resources Attached to Reasoning Process
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A Complex Query
What recent purchases of suspicious equipment has
XYZ Corp or its subsidiaries or parent firm
made in foreign countries?
parent(y,x)
illegal
not USA
Ask User
subsidiary(x,y)
Subsidiaries XYZ ABC, ... DEF ..., XYZ, ...
biowarfare
Purchase Agent XYZ, ABC, DEF, ... Patient
anthrax, ... Date since Jun05 Location --
DB of bio-equip
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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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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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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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Abduction
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.