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Declarative Programming
PROLOG (+ Bayesian Nets)
Second part of Cmput325
Fall 2004
R Greiner + B Price
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Declarative Programming
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Motivation
 Warm Fuzzies
 What is Logic? ... Logic Programming?
Mechanics of Prolog
 Terms, Substitution, Unification, Horn Clauses, Proof process
Example: List Processing
Theoretical Foundations
 Semantics
 Logic / Theorem Proving … Resolution
Other Issues
Search Strategies
 Declarative/Procedural, ...
 “Impure'' Operators” --- NOT, !
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Utilities
? Constraint Programming
? Bayesian Belief Nets
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2004 … 1990 … 1980
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Story …
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MD sees patient … perhaps MENINGITIS!
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Performs standard tests
Calls Infection Disease (medical) expert
Dialogue:
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Expert asks for info re: patient
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Fever, Organism Morphology, Gram Stain, Spinal Fluid, …
Doctor's answers:
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DIRECT : from direct measurement, Lab tests
Qualitative: Has HIGH fever
Vague: Portal of Entry was GastroIntestinal (w/certainty 0.6)
Unknown: don’t know identity of organism?
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Story … con’t
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MD can ask questions:
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Why ask about portal of entry?
Expert answers:
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If further questioned, … point to definitive study
Expert provides DIAGNOSIS
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trying to show
infecting organism is ENTEROBACTERICAE
this information is crucial in that decision.
organism was one of {E.coli, Enterobacteria }
suggest TREATMENT: Give GENTAMICIN
Happily ever after...
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The Catch …
Expert System
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Expert System
An EXPERT SYSTEM is a computer program
that exhibits Expert Level performance in
solving complex problems.
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Reasons with Facts about the World:
Combines
 General Facts/Rules (about Diseases, ...)
with
 Specific Facts (about Patient)
to Produce new Conclusion (diagnosis)
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Medical Expert Systems
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MYCIN
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Glaucoma
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Kidney
Ventricle Movement
ONCOCIN
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Ventilator Management
ALVEN
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Erratic Heartbeat
VM
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Present lllness Program
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Digitalis advisor
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Internal Medicine
CASNET
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Blood Infections
CADUCEUS
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…
Cancer Treatment
Protocols
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Other Domains
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Medicine
Chemistry
Instruction
Job-Shop Management
Financial Planning
Computer Diagnosis, Configuration
VLSI Design
Molecular Genetics
Signal Analysis
Structural Mechanics
Mathematics
…
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“Declarative Programming''
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Give
Gentamycin?
Is 
true?
Knowledge Base
--- -- --- ---- --- - -- --- - --- ------ -- --- -Facts about the world
-- ---- --- ---- ----- - ----- -- ----- -- --- - -
Proof
Procedure
Yes … No
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Advantages of Framework
store “truths”
ask for other truths
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Simply
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Information is
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Modular
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Easy to Build
Easy to Modify (Extend, Debug)
Capable of Explanation
Declarative
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Re-use same info for different tasks
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Computers Manipulate SYMBOLS
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Numbers
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3, 5, ...
Addition, Multiplication, ...
Propositions
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“D1 is an inverter''
“Inverters flip bits''
...
Deduction, ...
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Simple Deduction
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Socrates is a man.
If Socrates is a man,
Then Socrates is mortal.
Socrates is mortal.
In general…
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Example of Deduction
(Goal)
Socrates is Mortal
R1
(New
Goal)
Socrates is a Man
RULES
R1: If Socrates is a Man,
Then Socrates is Mortal
o
o
FACTS
o
o
F1: Socrates is a Man.
o
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Example of Deduction, #2
R2
Plato is Mortal
Plato is a Cat
R1
Plato is a Man
R3
Plato purrs
RULES
R1: If Plato is a Man,
Then Plato is Mortal
R2: If Plato is a Cat
Then Plato is Mortal.
R3: If Plato purrs,
Then Plato is a Cat.
FACTS
o
o
F3: Plato purrs.
o
o
o
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Example of Deduction, #3
Aristotle is a man
R9
Aristotle is a Human
RULES
R2: If Plato is a Cat
Then Plato is Mortal.
o
R9: If Aristotle is a human
and Aristotle is male,
Then Aristotle is a man
o
Aristotle is male
FACTS
o
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F3: Aristotle is male.
o
F8: Aristotle is a human
o
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Oversimplified Proof Process
If Goal i = FACT
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then DONE
Else …
YES
Goal i = “Then Part” of Rule R
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then Goal i+1  “If Part” of R
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else DONE NO
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Just Manipulating Symbols
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Consider claim
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This is Belgium.
Conclusion is wrong!
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based on “proof”
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Today is Tuesday.
If
Today is Tuesday
Then This is Belgium.
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This is Belgium
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Conclusion is
ONLY AS TRUE
as PREMISES
If Premises true,
then Conclusion is.
Not fault of PROOF
process
GIGO…
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Rules
R1: if (1) You have a Parking Permit &
This space is Permit-Parkable,
then You can park at this space.
(2)
R2: if (1) This space is a Parking Space &
Permit-Sign at this space &
(3) Current date is Acceptable,
then This space is Permit-Parkable.
(2)
R3: if (1) Current time is 7am-Midnight &
This space is Permit-Parkable,
then You can park at this space.
(2)
R4: if
(1)
R5: if
(1)
Current month is Dec-Mar,
then Current date is Acceptable.
Current month is in Apr-Nov &
(2) Current day of month is ≤ 15
then Current date is Acceptable.
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Facts
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This space is a Parking Space.
You live near this space.
You have a Parking Permit.
Current month is in Apr-Nov.
Current day is Tuesday.
Current day of month is ≤ 15.
Permit-Sign at this space.
You own a car.
Your car is >5 years old.
Current time is 3am.
You have $18.00.
...
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Inference Graph
You can park at this space
R1
You have a Parking Permit
This space is Permit-Parkable
R2
… Parking Space
Current date is Acceptable
R5
Permit-Sign …
…Apr-Nov
… ≤ 15
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Additional Rules
R1: if
(1)
R2: if
(1)
You have a Parking Permit &
(2) This space is Permit-Parkable,
then You can park at this space.
This space is a Parking Space &
(2) Permit-Sign at this space &
(3) Current date is Acceptable,
then This space is Permit-Parkable.
R7: if
(1)
R8: if
(1)
You live near this space &
(2) You own a car &
(3) You apply for a permit,
then You have a Parking Permit.
You can park at this space
then You can take a car.
R3: if (1) Current time is 7am-Midnight &
This space is Permit-Parkable,
then You can park at this space.
(2)
R4: if
(1)
R5: if
(1)
Current month is Dec-Mar,
then Current date is Acceptable.
Current month is in Apr-Nov &
(2) Current day of month is ≤ 15
then
Current date is Acceptable.
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Inference Graph
You can take a car
R8
You can park at this space
R1
You have a Parking Permit
This space is Permit-Parkable
R2
R7
… Parking Space
… live near …
… apply for permit
Current date is Acceptable
R5
Permit-Sign …
…own a car
…Apr-Nov
… ≤ 15
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Mycin: What is the suspected portal of entry of ORGANISM-1 into
this sterile site?
Doctor: WHY
Mycin: [ie, why is it important to determine the … site?]
[3.0] … to determine which organism(s) to cover …
It has already been established that
3.1] site of culture is blood
3.2] organism stain is gram positive
Therefore, if
3.3] portal of entry is g.i.
3.4] locus of infection is Pelvis or Abdomen,
Then
 strongly suggestive evidence (0.9) that therapy
should cover enterobacteriaceae.
[Rule 095]
...
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Mycin: What is the suspected portal of entry of ORGANISM-1 into
this sterile site?
Doctor: WHY
Mycin: [ie, why is it important to determine the … site?]
[3.0] … to determine which organism(s) to cover …
If has already been established that
3.1] site of culture is blood
3.2] organism stain is gram positive
Therefore, if
3.3] portal of entry is g.i.
3.4] locus of infection is Pelvis or Abdomen,
Then
 strongly suggestive evidence (0.9) that therapy
should cover enterobacteriaceae.
[Rule 095]
...
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Advantage of Rule Transparency
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Explain reasoning
Support / Credability
Helpful when…
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building/extending system
modifying system
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Issues
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Faster Computation
User Interaction
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Focus of Attention
“Human Engineering”
Variables
Control of Search
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Which (sub)goal? Which rule?
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Variables
You can park at
RL
RA
RB
X = SpaceA
X = SpaceB
RA: if
…,
then Can park @ SpaceA.
o
o
o
(1)
X
RB: if
X = ParkingLot-L
…,
RL: if (1) …,
then Can park @ SpaceB. then Can park @ Lot-L.
o
o
o
o
o
o
(1)
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Control of Search
FACTS
F1:
F2:
F3:
RULES
f( Abe, Bob )
f( Bob, Charles )
f( Charles, Dave )
R1:
R2:
a( x, y ) & a( y, z )  a( x, z )
f( x, y )  a ( x, y )
a(Abe, Dave)
R1
a(Abe, y1)
R1
a(Abe, y2)
R1
a(Abe, y3)
R2
a( y1, Dave)
f(Abe, Dave)
R2
a(y2, y1)
f(Abe, y1)
R2
a(y3, y2)
f(Abe, y2)
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Research Issues
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Better Decision Making
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“Deeper Knowledge”
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Coping with Uncertainty
Better Explanation
First Principles
“Meta”
Acquiring the Knowledge
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… from expert
… from data
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