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8/2/2019 Perception-based Intelligent Decision Systems
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PERCEPTION-BASED INTELLIGENT DECISION SYSTEMS
Lotfi A. Zadeh and Masoud Nikravesh
Computer Science Division Department of EECS
UC Berkeley
URL: http://www-bisc.cs.berkeley.edu
URL: http://zadeh.cs.berkeley.edu/
Email: Zadeh@cs.berkeley.edu and Nikravesh@cs.berkeley.edu
ONR Summer 2002 Program Review UCLA, July 30-August 1
LAZ 7-31-02
http://www-bisc.cs.berkeley.edu/http://zadeh.cs.berkeley.edu/mailto:Zadeh@cs.berkeley.edumailto:Nikravesh@cs.berkeley.edumailto:Nikravesh@cs.berkeley.edumailto:Zadeh@cs.berkeley.eduhttp://zadeh.cs.berkeley.edu/http://www-bisc.cs.berkeley.edu/http://www-bisc.cs.berkeley.edu/http://www-bisc.cs.berkeley.edu/8/2/2019 Perception-based Intelligent Decision Systems
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BASIC GOAL
CONCEPTION, DESIGN AND IMPLEMENTATION OF INTELLIGENT
DECISION SYSTEMS
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BASIC STRUCTURE
acquisition of information
communication of information
processing of information (extracting decision-relevant information)
decision
execution
assessment
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INTELLIGENT DECISION SYSTEM
INFORMATION-ON-DEMAND MODULE
INFORMATION PROFFERAL MODULE
INFORMATION ALERT MODULE
INFORMATION-ON-DEMAND MODULE=Q/A SYSTEM
Q/A SYSTEM=SEARCH ENGINE + DEDUCTION MODULE
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primary goal secondary goal
BASIC GOAL
development of new tools for solving existing and
new problems
use of new tools for solving existing and new
problems
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CONTENTION coordinated management of multi-agent
decision systems is beyond the capabilities of measurement-based methods
the problem is analogous to driving a car in heavy city traffic
humans can do this without any measurements and any computations, using perceptions of distance, speed, position intent and other decision-relevant variables and parameters
automation of driving in heavy city traffic is beyond the capabilities of existing
measurement-based systems LAZ 7-22-02
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TRANSFORMATION OF VISIONS INTO REALITY
needed: addition to the existing,
measurement-based, methods of the capability to operate and base decisions on perception-based information
it is this essential capability that humans have and machines have not
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THE TRIP-PLANNING PROBLEM
I have to fly from A to D, and would like to get there as soon as possible I have two choices: (a) fly to D with a connection in B; or
(b) fly to D with a connection in C
if I choose (a), I will arrive in D at time t 1 if I choose (b), I will arrive in D at time t 2 t 1 is earlier than t 2
therefore, I should choose (a) ?
A
C
B
D
(a)
(b)
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CONTINUTED now, let us take a closer look at the problem the connection time, c B , in B is short should I miss the connecting flight from B to D, the next flight will bring me to D at t 3 t 3 is later than t 2
what should I do?
decision = f ( t 1 , t 2 , t 3 ,c B ,c C )
existing methods of decision analysis do not have the capability to compute f
reason: nominal values of decision variables
observed values of decision variables LAZ 7-30-02
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CONTINUED
the problem is that we need information about the probabilities of missing connections in B and C.
I do not have, and nobody has, measurement-based information about this probabilities
whatever information I have is perception-based
with this information, I can compute perception-based granular probability distributions of arrival times in D for (a) and (b)
the problem is reduced to ranking of granular probability distributions
Note: subjective probability = perception of likelihood
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PERCEPTION-BASED GRANULAR PROBABILITY DISTRIBUTION
A1 A2 A3
P 1
P 2 P 3
arrival time (AT)
probability
P(AT) = P 1\A1 + P 2 \A2 + P 3 \A3
Prob {AT is A i } is P i
0
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NEW TOOLS
CN
IA GrC PNL
CW + + +
computing
with numbers
computing with intervals
computing with granules
precisiated natural language
computing
with words
PTp CTP: computational theory of perceptions
PTp: perception-based probability theory
THD: theory of hierarchical definability
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CTP THD a granule is defined by a generalized constraint
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COMPUTING WITH WORDS
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CW AND PNL a concept which plays a central role in CW is that
of PNL (Precisiated Natural Language) basically, a natural language, NL, is a system for
describing perceptions
perceptions are intrinsically imprecise imprecision of natural languages is a reflection of
the imprecision of perceptions the primary function of PNL is that of serving as a
part of NL which admits precisiation PNL has a much higher expressive power than
any language that is based on bivalent logic
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COMPUTING WITH WORDS (CW) in computing with words, the objects of
computation are words and propositions in a natural language example: a box contains N balls of various sizes
a few are small
most are medium a few are large how many are neither small nor large
example: A is near B B is near C how far is A from C
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KEY POINTS words are less precise than numbers
computing with words (CW) is less precise than computing with numbers (CN)
CW serves two major purposes a) provides a machinery for dealing with
problems in which precise information is not available
b) provides a machinery for dealing with problems in which precise information is
available, but there is a tolerance for imprecision which can be exploited to achieve tractability, robustness, simplicity and low solution cost
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PRECISIATED NATURAL LANGUAGE
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WHAT IS PRECISIATED NATURAL LANGUAGE (PNL)? PRELIMINARIES
a proposition, p, in a natural language, NL,
is precisiable if it translatable into a
precisiation language in the case of PNL, the precisiation
language is the Generalized Constraint
Language, GCL precisiation of p, p*, is an element of GCL
(GC-form)
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WHAT IS PNL?
PNL is a sublanguage of precisiable propositions in NL which is equipped with two dictionaries: (A) NL to GCL; (B) GCL to PFL (Protoform Language); and (C) a collection of rules of deduction (rules of generalized
constrained propagation) expressed in PFL.
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PRECISIATED NATURAL LANGUAGE (PNL)
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NLGCL
generalized constraint form of type r
p X isr R translation
generalized constraint form of type r (GC(p))
LAZ
p translation
precisiation language (GCL)
precisiation explicitation
GC-form CSNL
precisiable propositions
in NL
p*
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DICTIONARIES A:
most Swedes are tall Count (tall.Swedes/Swedes) is most
p p* (GC-form)
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proposition in NL precisiation
B:
Count (tall.Swedes/Swedes) is most
p* (GC-form)
protoform precisiation PF(p*)
Q As are Bs
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PNL AND THE COMPUTATIONALTHEORY OF PERCEPTIONS
in the computational theory of perceptions (CTP), perceptions are dealt with through their descriptions in a natural language
perception = descriptor(s) of perception
a proposition, p, in NL qualifies to be an object of computation in CTP if p is in PNL
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EXAMPLE I am driving to the airport. How long will it
take me to get there? Hotel clerks perception -based answer:
about 20-25 minutes about 20 - 25 minutes cannot be defined
in the language of bivalent logic and probability theory
To define about 20 - 25 minutes what isneeded is PNL
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DEFINITION OF p: ABOUT 20-25 MINUTES
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time
time
time
time
20 25
20 25
20 25
A
P
B
6
0
1
0
0
1
1c-definition:
f-definition:
f.g-definition:
PNL-definition: Prob (Time is A) is B
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EXAMPLE PNL definition of about 20 to 25 minutes
Prob {getting to the airport in less than about 20 min} is unlikely Prob {getting to the airport in about 20 to 25 min} is likely Prob {getting to the airport in more than 25 min} is unlikely
granular probability distribution
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P
likely
unlikely
Time 20 25
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COMPUTATIONAL THEORY OF PERCEPTIONS
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COMPUTATIONAL THEORY OF PERCEPTIONS (CTP) PREAMBLE
It is a deep-seated tradition in science to equate scientific progress to progression from perceptions to measurements
But, what humans have and machines have not is a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. A canonical example of this capability is driving in heavy city traffic. Another example is summarizing a book
To endow machines with this capability it is necessary to
progress, countertraditionally, from measurements to perceptions
This is the objective of the computational theory of perceptions (CTP) a theory in which perceptions are objects of computation
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FROM MEASUREMENTS TO PERCEPTIONS
WINE EXPERT assessment sample
chemical analysis
NN excellent
perception
fuzzy measurements neural network
crisp input
wine excellent
perception
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NN is a neurofuzzy neural network
with crisp input and fuzzy output
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COMPUTATIONAL THEORY OF PERCEPTIONS
the point of departure in the computational theory of perceptions is the assumption that perceptions are described by propositions expressed in a natural language
examples economy is improving Robert is very honest it is not likely to rain tomorrow
it is very warm traffic is heavy
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in general, perceptions are summaries perceptions are intrinsically imprecise
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CONTINUED imprecision of perceptions is a manifestation of
the bounded ability of sensory organs and,ultimately, the brain, to resolve detail and store information
perceptions are f-granular in the sense that (a) the boundaries of perceived classes are fuzzy; and (b) the values of perceived attributes are granular, with a granule being a clump of values drawn together by indistinguishability, similarity,proximity or functionality
it is not possible to construct a computational theory of perceptions within the conceptual
structure of bivalent logic and probability theory LAZ 7-22-02
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it is 35 C Eva is 28 Tandy is three years
older than Dana
It is very warm Eva is young Tandy is a few
years older than Dana it is cloudy traffic is heavy Robert is very honest
INFORMATION
measurement-based numerical
perception-based linguistic
MEASUREMENT-BASED VS. PERCEPTION-BASED INFORMATION
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CONTINUED
with probability 0.9
Robert returns from work between 5:45pm and 6:15pm.
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usually Robert returns from work at about 6 pm
the mathematics of perception-based information has a higher level of generality than the mathematics of measurement-based information
a proposition is a perception if it contains fuzzy quantifiers: many, most, few, ; fuzzy qualifiers: usually,
probably, possibly, typically, generally, ; fuzzy modifiers: very, more or less; extremely, ; and/or fuzzy nouns, adjective or adverbs,
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PERCEPTION OF A FUNCTION
LAZ 7-22-02
if X is small then Y is small if X is medium then Y is large if X is large then Y is small 0
X
0
Y
f f* : perception
Y
f* (fuzzy graph)
medium x large
f
0
S M L
LM S
granule
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DEDUCTION (COMPUTING) WITH PERCEPTIONS
deduction
example
p 1
p 2
p n
P n+1
Dana is young Tandy is a few years older than Dana
Tandy is (young+few)
deduction with perceptions involves the use of protoformal rules of generalized constraint propagation
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PROTOFORM LANGUAGE
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THE CONCEPT OF PROTOFORM protoform=abbreviation of prototypical form
syntactic parse
semantic parse
syntax tree
logical form
semantic network
conceptual graph
canonical form
p parsing
semantic parse protoform 1 protoform 2 abstraction abstraction
protoform 3
protoform=abstracted summary
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THE CONCEPT OF PROTOFORM a protoform is an abstracted prototype of a class of
propositions
examples: most Swedes are tall
many Americans are foreign-born
overeating causes obesity Q As are Bs
obesity is caused by overeating Q Bs are As
Q As are Bs
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P-abstraction
P-abstraction
P-abstraction
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WHAT IS A PROTOFORM p=proposition in a natural language if p has a logical form, LF(p), then a protoform of p, PF(p),
is an abstraction of LF(p)
all men are mortal x(man(x) mortal(x)) x(A(x) B(x))
abstraction=deinstantiation
all men are mortal all men are A
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abstraction deinstantiation
p LF(p) PF(p)
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CONTINUED if p does not have a logical form but is in PNL,
then a protoform of p is an abstraction (deinstantiation) of the generalized constraint form of p, GC(p)
most Swedes are tall Count(tall.Swedes/Swedes) is most
p GC(p)
QAs are Bs
PF(p)
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abstraction
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EXAMPLES
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N L LOGICAL FORM PROTOFORM
all men are mortal
most Swedes are tall
usually Robert
returns from work at about 6pm
Vx(man(x) mortal(x)) Vx(A(x) B(x))
Q As are Bs
Prob (A) is B
fuzzy event
fuzzy probability
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ORGANIZATION OF KNOWLEDGE
much of human knowledge is perception-based examples of factual knowledge
height of Eiffel Tower is 324 m (with antenna) (measurement-based)
Berkeley is near San Francisco (perception-based) icy roads are slippery (perception-based) if Marina is a student then it is likely that Marina is young
(perception-based) LAZ 7-22-02
FDB DDB
factual database deduction database fact rule
measurement-based perception-based
knowledge
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PROTOFORM AND PF-EQUIVALENCE
P is the class of PF-equivalent propositions P does not have a prototype P has an abstracted prototype: Q As are Bs P is the set of all propositions whose protoform is: Q As are Bs
knowledge base (KB)
PF-equivalence class (P)
P q
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protoform (p): Q As are Bsmost Swedes are tall
few professors are rich
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PROTOFORMAL CONSTRAINT PROPAGATION
Dana is young Age (Dana) is young X is A
p GC(p) PF(p)
Tandy is a few years older than Dana
Age (Tandy) is (Age (Dana)) Y is (X+B)
X is AY is (X+B) Y is A+B
Age (Tandy) is (young+few)
)-()((sup)( uvuv B Au B A
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+few
REASONING WITH PERCEPTIONS
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REASONING WITH PERCEPTIONS: DEDUCTION MODULE
GC-form GC(p)
perceptions p
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GC-forms GC(p)
terminal data set
terminal protoform
set
initial protoform
set
protoforms PF(p)
translation explicitation precisiation
IDS IGCS
initial data set initial generalized
constraint set
IGCS IPS
TPS TDS IPS
abstraction deinstantiation
goal-directed deduction
deinstantiation
initial protoform set
DEDUCTION MODULE
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DEDUCTION MODULE rules of deduction are rules governing
generalized constraint propagation
rules of deduction are protoformal examples generalized modus ponens
X is A
if X is B then Y is C Y is A o (B C) )),()(sup()( vuuv C B A y
Prob (A) is B
Prob (C) is D
LAZ 7-22-02
)))()(((sup)( duu guvU
A B g D
subject to duu guv
U
C )()(
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EXAMPLE OF DEDUCTION
most Swedes are tall ? R Swedes are very tall
most Swedes are tall Q As are Bs s/a-transformation
Q As are Bs
Q 1/2 As are 2 Bs
most 1/2 Swedes are very tall r 1
1
0 0.25 0.5
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most 1/2
most
CONTINUED
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CONTINUED
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not(QAs are Bs) (not Q) As are Bs
Q 1 As are Bs Q 2 (A&B)s are Cs
Q 1 Q 2 As are (B&C)s
Q 1 As are Bs Q 2 As are Cs
(Q 1 + Q 2 - 1) As are (B&C)s
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INFORMAL PROTOFORM-BASED REASONING
most As are BsX is Ait is likely that X is B
QAs are Bs X is A
Prob(X is B) is Q
tacit assumptions: X is picked at random from As LAZ 7-22-02
COUNT AND MEASURE RELATED RULES
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COUNT- AND MEASURE-RELATED RULES
Q As are Bs
ant (Q) As are not Bs r 0
1
1
ant (Q)
Q
Q As are Bs
Q 1/2 As are 2 Bs r 0
1
1
Q
Q 1/2
most Swedes are tall ave (tall |Swedes) is ?h
Q As are Bsave (B|A) is ?C
LAZ 7-22-02
))(1
(sup)( i BiQaave a N v
)(1
iia
N v
),...,( 1 N aaa,
crisp
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THE ROBERT EXAMPLE
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THE ROBERT EXAMPLE
the Robert example relates to everyday commonsense reasoning a kind of reasoning which is preponderantly perception-based
the Robert example is intended to serve as a test of the deductive capability of a
reasoning system to operate on perception-based information
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THE ROBERT EXAMPLE
Version 1.My perception is that Robert usually returns from work at about 6:00pm
q 1 : What is the probability that Robert is home at about t pm?
q 2 : What is the earliest time at which the probability that Robert is home is high?
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THE ROBERT EXAMPLE (VERSION 3)
IDS: Robert leaves office between 5:15pm and 5:45pm. When the time of departure is about 5:20pm, the travel time is usually about 20min; when the time of departure is about 5:30pm, the travel time is usually about 30min; when the time
of departure is about 5:40pm, the travel time is about 20min
usually Robert leaves office at about 5:30pm
What is the probability that Robert is home at about t pm?
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THE ROBERT EXAMPLE
Version 4 Usually Robert returns from work at about 6 pm
Usually Ann returns from work about half-an-hour later What is the probability that both Robert and Ann are home at about t pm?
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1
0 6:00 t time
Robert Ann P
THE ROBERT EXAMPLE
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THE ROBERT EXAMPLE
event equivalence
Robert is home at about t pm= Robert returns from work before about t pm
LAZ 7-22-02
1
0 T t time
time of return
before t*
t* (about t pm)
Before about t pm= o about t pm
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THE ROBERT EXAMPLE
LAZ 7-22-02
backtracking from query to query-relevant information
query (q) : what is the probability,P, that Robert is home at about t pm (t*)?
query (q) : what is the earliest time at which the probability that Robert is home is high?
Version 1
query-relevant information (q 1 ): probability distribution of time, T, at which Robert returns from work
relevant fact (f(q -1 ): usually Robert returns from work at about 6pm
CONTINUED (VERSION 1)
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CONTINUED (VERSION 1) Q: what is the probability that Robert is home at t*?
CF(q): duu gu t )()(12
0*
LAZ 7-22-02
is ?P
PF(q): Prob(C) is ? D
0
1
6 pm t time
* t
t*
KB
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CONTINUED
Prob (C) is D
Prob (A) is B
KB FDB DDB
LAZ 7-22-02
Q -1
P(C) is ?D P(A) is ?B
q
protoformal rule in DDB
Prob (C is D)
Prob (A is B) Prob (C is D) Prob (Robert returns from
work at about t) is usually instantiation
duuqut )()(12
0
* is usually
PROBABILISTIC CONSTRAINT PROPAGATION RULE
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PROBABILISTIC CONSTRAINT PROPAGATION RULE (a special version of the generalized extension principle)
duuu g AU )()( is R
duuu g BU )()( is ?S
)))()(((sup)( duuugv AU RgS
subject to
1)(
)()(
duu g
duuu gv
U
BU
LAZ 7-22-02
CONTINUATION
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CONTINUATION P : membership function of P
generalized extension principle
LAZ 7-22-02
(u)du))g(u) ((max=(v) *612
0usuallygP
subject to: g(u)du(u)=v *t
12
0
1=g(u)du12
0
THE BALLS IN BOX EXAMPLE
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THE BALLS-IN-BOX EXAMPLE a box contains N balls of various sizes
my perceptions are:
a few are small most are medium a few are large
a ball is drawn at random
what is the probability that the ball is neither small nor large
LAZ 7-22-02
IDS (initial data set)
PERCEPTION BASED ANALYSIS
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PERCEPTION-BASED ANALYSIS
a few are small Count(small) is few Q 1 As are B 1s
most are medium
a few are large
Count(medium) is most Q 2 As are B 2 s
Count(large) is few Q 3 As are B 3 s
} u ,...,{u = A n1
LAZ 7-22-02
; u i =size of i th ball; u= ( u 1, , u n )
: ) u ,...,(u n11 possibility distribution function of (u 1, , u n ) induced by the protoform Q 1 As are Bs
))(u (-)u,...,(u1111 i BiQn
1
N 1
N 1
N
1N
CONTINUED
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CONTINUED : ) u ,...,(u n1 possibility distribution function induced by IDS
) u ,...,(u ) u ,...,(u ) u ,...,(u ) u ,...,(u n 1312111
query: (proportion of balls which are neither large nor small) is? Q 4
)) ( (1 ) (u ((1 = Q irgmall -4
protoformal deduction rule (extension principle)
(u)) (u) (u) ( sup = (v) 3214
subject to
LAZ 7-22-02
))) (u (1 )) ( ((1 = V i- 311N
1N
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CONCLUSION
the goal of realization of an intelligent multi- agent decision system is beyond the capabilities of measurement-based systems
to achieve the goal, it is necessary to employ systems which have the capability to operate on perception-based information
CW, PNL and CTP are necessary tools for adding this capability to measurement-based systems
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