Artificial Intelligence Programming Atsushi Inoue

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Artificial Intelligence ProgrammingAtsushi Inoue
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Objectives

• Start with what you learned in Data Structures.
• Objective 1 Identify the structures of programs
  developed in Artificial Intelligence.
• Objective 2 Identify advantages of using
  programming languages primarily developed for
  Artificial Intelligence (comparing to OOPL, Imp.
  Lang.)
• Functional Programming Language (Scheme)
• Logic Programming Language (FRIL)

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Problem-Solving for AI

• General problem-solving framework for computer
  science data structure algorithm program
• AI configuration solver

Framework Configuration Solver State Space
Search Graph/Network Search Algorithms GA Gen
e GA/GP/EC NN Network Signal
Propagations KBS Cases/Rules Reasoning/Learni
ng
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List, Tree and Graph

• Problems are configured within networks, gene,
  cases, and rules for appropriate solvers.
• How are they represented within programs?
• Networks, strings (gene), tuples (cases),
  predicates/propositions (rules) are generated
  within lisp processing frameworks (array,
  linked-list).
• How solvers solve problems?
• Traverse such lists. (various searching
  algorithms)
• Find and/or generate solutions.

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It is like a maze, isn't it?
Maze can be represented as a graph (network) and
can be solved as network search.
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Backtracking
While treasures are NOT found OR give them up,
keep searching!!
Bounded (dead end) Backtrack!!
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Example sum of subset

• S a set of integers
• Problem find a subset of S whose sum is X.
• Approach Backtracking
• Keep taking numbers until the sum gt X.
• Throw the last number if the sum gt X.
• Keep going until a subset whose sum X(or all
  subsets have been searched).
• Bounded condition the sum gt X

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Implementation of Backtracking

• Representation
• Note an integer
• Path a sum
• Graph Search Bounded Condition
• Consider DFS Bounded Condition
• Q what if BFS instead?Any difference?

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Other Examples

• Classroom assignments
• Course teaching schedules
• GANT/PART/CPM
• Solving puzzles
• Making travel itinerary
• Navigating a good route to a destination(Navigati
  on systems)
• ...... many others

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Functional Programming
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What is Functional Programming?

• List Functions Program
• Originated with LISP by J. McCarthy in 1958
• Storage management garbage collection (GC)
• Intended to be First-class functions
• Functions can be retrieved and stored as values
• Functions can be passed as arguments
• Functions can be returned as the result
• Languages LISP, Scheme, ML

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Scheme

• MIT Scheme
• http//www.swiss.ai.mit.edu/projects/scheme/
• Simple about 50 US-letter pages of specification
  (R5RS Revised 5 Report on the Algorithmic
  Language Scheme)
• Complete smallest ambiguities among
  implementations for different platforms
• Rich Lib. Window management, RDB, OOP.,
  Networks, etc.
• EWU CS
• http//penguin.ewu.edu/class/ai/modules/tool2/

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Comparison
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Scope of Variables
Global x 1
Global x 1
Func2 use x
Func1 para x call Func2
Func2 use x
Func1 para x call Func2 use x
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First-Class Function
passed as an argument
returned and stored as a value
(define func (gen-func )) gt func (func 6 2)
gt 12?
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Cons Cell List Processing
Pointing to a symbol or another cons cell
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Higher Order Function Mapping
f
Domain
Range
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Stream-Oriented Computing
Consider a sequence with a recurrent
relation e.g. fibonacci fibi fibi-1 fibi-2
where i gt 2 0 1 1 2 3 5 8 13 21 34 55 (stream
of Fibonacci)
0
1
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Object-Oriented Programming
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Logic Programming
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Logic

• Mathematics, Philosophy, ...We are interested in
  how computers can handle logic.
• Reviewing discrete math., we know
• Propositional logic
• Predicate logic
• Proof as a chain of inference rules deduction
  ()
• How about others such as induction, proof by
  contradiction, .... Do you remember?

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Proposition Predicate

• Proposition a, b, .... (no arguments, i.e.
  independent variables)
• Predicate human(X) parent(X, Y) for all X,
  there exists Y
• Quantification of variables existential (there
  exists), universal (for all)
• Inference process for predicate logic
• Propositionalization substitute all variables
  in predicates --gt propositions
• Universal instantiation substitute universally
  quantified variables
• Exsistential instantiation (Skolemization)
  substitute existentially quantified variables
• Unification process of finding satisfiable
  substitutions
• Resolution obtain shorter, more specific clause
  from known multiple clauses
• First-Order Logic (FOL) quantified variables
  appear ONLY in arguments of predicates. (whereas
  higher-order logic quantifies predicates
  themselves)

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Inference Rules

• Modus Ponens a, a -gt b b
• Modus Tollence not b, a -gt b not a
• And Introduction a, b a b
• And Elimination ab a, b
• Generalized Modus Ponens (Modus Ponens
  Unification) in FOL
• Lifting opposite from propositionalization Pro
  positional logic to predicate logic, in many
  cases, FOL
• Many more (mostly composite) inference rules

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Aspects of Process

• Syllogism a path to consequence drawn by
  inference rules from what are known (chain of
  resolutions).
• A B C ..... (A, B, C are sets of logical
  exp.)
• Proof Search (i.e. infer/reason) a path (i.e.
  syllogism) from what are known to (desired)
  consequence by constructing syllogisms consisting
  of inference rules (resolution, unification,
  etc.)
• How can we automate such process?

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Backtracking Approach

• Consider syllogisms as paths within a network.
• We perform network search for a proof, i.e a
  search for a syllogism (path).
• We use 'inference rules' (a resolution) for each
  transformation (i.e. a link)
• Such ideas are called automated theorem proof and
  automated reasoning

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Computational Logic

• Study on Logic represented and processed
  (reasoning/inference) on computer systems.
• Proof as network search problems
• Computational complexity? may be intractable!!
• So, we know that automated theorem proof is hard,
  BUT we can still utilize such study for many
  purposes (e.g. expert systems, intelligent
  controls, logic programming)

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Logic Programming

• Programs are written in logic
• Logic (Program) Control (Query Process)
  Algorithm
• Language PROLOG, FRIL, and many others....
• Subset of computational logic featuring
• Unit resolution resolve one literal (predicate)
  in a query (a collection of literals/predicates)
  at a time.
• Limit of clauses in the form of C if AB...I...
  (Horn Clause HC) makes the unit resolution
  'complete' (i.e. Finite steps in proof can be
  found if it can be proven.)
• Such specification makes processes tractable, but
  STILL as expressive as FOL

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Why Logic Programming?

• Why is it advantageous?
• Partial answers
• Powerful representation high abstraction
• Simple and natural syntax (i.e. logic!!)
• Small programs (high readability, easy
  maintenance, easy optimization) the same sense
  as SQL
• And more .....
• Are they widely used? Not as programming
  language, but as a foundation of KBS, DB Query,
  PS, etc.

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FRIL

• Fuzzy Relational Inference Language
• Logic Programming Language with
• Features of PROLOG
• Support Logic Programming (probability intervals)
• Fuzzy Sets within SLP (mass assignment theory)
• Evidential Logic Programming (weight aggregation)
• S-expression efficient notation (like
  LISP/Scheme)
• EWU CS
• http//penguin.ewu.edu/class/ai/modules/tool1/
• http//penguin.ewu.edu/class/ai/modules/aim16/fril
  src/suppquery.frl

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How Logic Programming Works

• Program a collection of HC's (declarative)
• Facts in HC with empty hypotheses
• Implications in HC with hypotheses
• Execution
• Query a list of predicates
• Query Processing Backtracking (DFSBounded
  Cond.)
• While predicates in the query are NOT satisfied
  OR no more alternatives to satisfy them keep
  searching the fact or the satisfaction
  of subquery (recursion)
• Bounded Cond. if subquery failed (backtracking
  alternatives)

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Very Simple (Meaningless) Example

• Knowledge Base (what we know)
• A lt- B C D
• B (lt- (empty))
• C lt- E F, C lt- H
• D lt- G
• E, F, G, H
• Query (what is asked)
• ?A (is A true?)

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Query Processing
A lt- B C D
DFS top to bottom left to right
D lt- G
C lt- E F
FRIL Code (one clause per line index) a1
((a)(b)(c)(d)) A lt- B C D b1 ((b)) c1
((c)(e)(f)) C lt- E F c2 ((c)(h)) C lt-
H d1 ((d)(g)) D lt- G e1 ((e)) f1
((f)) g1 ((g)) h1 ((h))
FRIL Query ?((a)) yes tq((a)) trace
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Starting Fril Trace - header gives (Clause-name
Index Nth-goal-in-body Depth) (top-level 1
0) (a) trace ?y (a 1 1 1) (b) trace
?y (a 1 1 1) SOLVED (b) (a 1 2 1) (c)
trace ?y (c 1 1 2) (e) trace ?y (c 1 1 2)
SOLVED (e) (c 1 2 2) (f) trace ?y (c 1 2
2) SOLVED (f) (a 1 2 1) SOLVED (c) (a 1 3 1)
(d) trace ?y (d 1 1 2) (g) trace
?y (d 1 1 2) SOLVED (g) (a 1 3 1) SOLVED
(d) (top-level 1 0) SOLVED (a)
A1 A lt- B C D
C1 C lt- E F
D1 D lt- G
(top,,1, 0)
Depth 0
(a,1,3,1)
(a,1,1,1)
(a,1,2,1)
Depth 1
(c,1,2,2)
(d,1,1,2)
(c,1,1,2)
Depth 2
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Append Hypotheses and Query

• ?a alt-bcd
• ?bcd b
• ?cd clt-ef
• ?efd e
• ?fd f
• ?d dlt-g
• ?g g
• ?ltemptygt yes

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What if C1 fails but C2 succeeds?
A lt- B C D
DFS top to bottom left to right
D lt- G
C lt- E F
FRIL Code (one clause per line) a1
((a)(b)(c)(d)) A lt- B C D b1 ((b)) c1
((c)(e)(f)) C lt- E F c2 ((c)(h)) C lt-
H d1 ((d)(g)) D lt- G e1 ((e)) f1
((f)) g1 ((g)) h1 ((h))
FRIL Query ?((a)) tq((a)) trace
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Starting Fril Trace - header gives (Clause-name
Index Nth-goal-in-body Depth) (top-level 1 0)
(a) trace ?y (a 1 1 1) (b) trace
?y (a 1 1 1) SOLVED (b) (a 1 2 1) (c)
trace ?y (c 1 1 2) (e) (c 1 1 2) FAILED
(e) - no definition for e (c 2 1 2) (h)
trace ?y (c 2 1 2) SOLVED (h) (a 1 2 1) SOLVED
(c) (a 1 3 1) (d) trace ?y (d 1 1 2)
(g) trace ?y (d 1 1 2) SOLVED (g) (a 1 3
1) SOLVED (d) (top-level 1 0) SOLVED (a)
(top,,1, 0)
Depth 0
(a,1,3,1)
(a,1,1,1)
(a,1,2,1)
Depth 1
Backtrack
(c,2,1,2)
(c,1,1,2)
(d,1,1,2)
Depth 2
FAILED
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Append Hypotheses and Query

• ?a alt-bcd
• ?bcd b
• ?cd clt-ef
• ?efd ltfailedgt because no e ? backtrack!!
• ?cd clt-h
• ?hd h
• ?d dlt-g
• ?g g
• ?ltemptygt yes

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What if both are satisfied?

• Suppose there are two options C1 and C2.
• Both satisfy the (sub)query ?((c))
• Why C1 is picked instead of C2?
• Answer order of clauses (i.e. C1 is defined
  prior to C2)
• Is there an option to perform a query for all
  possible solutions? The answer is YES!!

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Universal Query

• ?((a)(fail)) is 'a' true the query fails?
• Response no of course not, because this query
  succeeds as we know. How is it processed?
• tq((a)(fail)) we trace this query.
• In summary, the predicate (fail) 'negation as
  failure'. The goal is never satisfied and thus
  causes for FRIL to backtrack.
• How useful is this? Quite useful but not now.

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Starting Fril Trace - header gives (Clause-name
Index Nth-goal-in-body Depth) (top-level 1 0)
(a) trace ?y ..... (c 1 1 2) (e)
trace ?y (c 1 1 2) SOLVED (e) ..... (top-level
1 0) SOLVED (a) (top-level 2 0)
(fail) (top-level 2 0) FAILED (fail) (d 1 1 2)
FAILED (g) (a 1 3 1) FAILED (d) (c 1 2 2) FAILED
(f) (c 1 1 2) FAILED (e) (c 2 1 2) (h)
trace ?y (c 2 1 2) SOLVED (h) ..... (top-level
1 0) SOLVED (a) (top-level 2 0)
(fail) (top-level 2 0) FAILED (fail) (d 1 1 2)
FAILED (g) (a 1 3 1) FAILED (d) (c 2 1 2) FAILED
(h) (a 1 2 1) FAILED (c) (a 1 1 1) FAILED
(b) (top-level 1 0) FAILED (a)
Proof with C1
Backtrack by (fail)
Proof with C2
Backtrack by (fail)
No more alternatives
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I thought FRIL looks more complex...

• Mainly because of arguments in predicates.
• Arguments constants variables.
• How are they handled in logic programming?
• Unification substitutions of variables with
  corresponding values/variables.
• List processing same principle as functional
  programming languages(notation (HT) for FRIL,
  HT for PROLOG)

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List Processing
(1 2 3 4)
Text
(HT)
Diagram
T
1
H
2
3
4
PROLOG
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FRIL Sum of Subset
((subsum () 0 ())) ((subsum (NL) SUM
(NSUBSUM)) (subsum L SUML
SUBSUM)(sum N SUML SUM)) ((subsum (NL) SUM
SUBSUM) (subsum L SUM
SUBSUM)) Fril gt?((subsum (1 2 2 4 5) 9 L)(pp
L)) (1 2 2 4) yes Fril gt?((subsum (1 2 2 4 5) 9
L)(pp L)(fail)) (1 2 2 4) (2 2 5) (4 5) no
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Starting Fril Trace .... (top-level 1 0)
(subsum (1 1 3) 4 _7) trace ?y (subsum 2 1
1) (subsum (1 3) _121 _120) trace
?y (subsum 2 1 2) (subsum (3) _204 _203)
trace ?y (subsum 2 1 3) (subsum () _2e7
_2e6) trace ?y (subsum 2 1 3) SOLVED (subsum () 0
()) (subsum 2 2 3) (sum 3 0 _204) (subsum
2 2 3) SOLVED (sum 3 0 3) (subsum 2 1 2) SOLVED
(subsum (3) 3 (3)) (subsum 2 2 2) (sum 1 3
_121) (subsum 2 2 2) SOLVED (sum 1 3 4) (subsum 2
1 1) SOLVED (subsum (1 3) 4 (1 3)) ...........
.............. (subsum 2 1 1) SOLVED (subsum (1
3) 3 (3)) (subsum 2 2 1) (sum 1 3
4) (subsum 2 2 1) SOLVED (sum 1 3 4) (top-level
1 0) SOLVED (subsum (1 1 3) 4 (1
3)) .........................
Unification
Unification
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Extension of Logic Programming
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Logic Programming with Probability

• Form of HC probability as a foundation of
  uncertainty management
• Example
• ((a))0.3 P(a)0.3
• ((b)(a))0.5 P(ba)0.5
• qs((b))((b)) (0.15 0.85) where does 0.85
  come from?No more solutionsyes

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Uncertainty Management Framework

• (Point) Probability
• e.g. P(x)0.3
• AIM12 Bayesian Belief Network
• Interval of Probability
• e.g. P(x)0.1, 0.5
• Support Logic (Base of FRIL)
• AIM13 Dempster-Shafer Theory of Evidence
• Fuzzy Probability
• e.g. P(x)high where ?high(P(x)) 0,1 -gt 0,1
• AIM14 Fuzzy Logic
• AIM15 Evidential Logic (Fuzzy-Neuro)

AIM16 Mass Assignment Theory
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Extension from point to interval

• Consider intervals of probabilities more
  uncertainty
• Support Logic Programming extension of logic
  prog.
• Example
• ((a)) (0.3 0.5) P(a)0.3, 0.5
• ((b)(a)) ((0.5 0.7) (0 1)) P(ba)0.5,
  0.7, P(bnot a)0, 1 (i.e. unknown)
• qs((b))((b)) (0.15 0.91)No more solutionsyes

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Special Case of Support Logic Prog.(Solution to
where 0.85 came from)

• Fully specified support logic programming in
  FRIL
• ((a))(0.3 0.3) P(a)0.3, 0.30.3
• ((b)(a))((0.5 0.5)(0 1)) P(ba)0.5, 0.50.5
  and P(bnot a)0, 1
• What if we do ... (to make SLP in FRIL Bayesian)
• ((a))0.3
• ((b)(a))((0.5 0.5)(0 0))
• qs((b)) yields ((b)) (0.15 0.15)

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General Case fuzzy predicates

• Consider predicates (propositions) with fuzzy
  sets.
• Example
• set(ud 0 10)
• (small 01 50 ud)
• (middle 00 51 100 ud)
• (large 50 101 ud)
• ((x is small)) (0.3 0.5)
• ((y is large)(x is middle))((0.3 0.5)(0 0))
• qs((y is X))((y3 is 50 101 )) (0 0.595)...

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Semantic Unification

• Unification of fuzzy propositions (i.e.
  instantiated predicates)
• Example
• X is small
• X is middle
• Application of mass assignment theory

A support (interval of probability) as the
degree of unification (i.e. Semantics are
provided in terms of fuzzy sets.
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Mass Assignment Theory
(Normal) fuzzy (sub)set
Consistency Management
Let e be an element of UD. m.s.v.(e)SUM_x, e in
x M(x) P(e)SUM_x, e in x M(x) SR(e, x) SR a
selection rule proportion of e within x (1/x
by default)
Mass Assignment is a generalization of measures
(e.g. probability and possibility membership
function of fuzzy set)
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Historical Background Uncertainty

• A long, long, ..., endless debate over souce and
  status of probability numbers for centuries (Game
  300BC? ... Bayes 17XX AD ... Probability and
  Logic 19xx AD ...)
• In 20th century, such debates became sharper so
  that we have frequentists, objectivists and
  subjectivists ...
• Many related theories belief, unitity, entropy,
  possibility, fuzzy logic, .....
• But, they are consistent with axioms of
  probability you learned in MATH380/385.

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Axioms of Probability

• a.k.a. Kolmogorov's axioms provides semantics
  of probabilities associated with propositions
• 0 lt P(a) lt 1 for any proposition a
• P(true)1, P(false)0
• P(a OR b)P(a)P(b)-P(a AND b) for any
  propositions a and b
• Probability theory is built upon this simple
  foundation.

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Jefferys Rule Foundation of SLP

• Consider two variables
• Hh, h
• Ee1, , en s.t. e1, , en are muturally
  exclusive and exhaustive
• P X -gt 0,1 (apriori probability)
• B X -gt 0,1 (belief based on experiences)
• Assume that conditional probabilities P(HE) are
  known
• B(h) ? e in E, P(he)B(e), B(h) ? e in E,
  P(he)B(e)
• B(x) and P(x) are not necessarily related.
• This can be B(x)P(x) (the case of probability)
• Base of Inference in Support Logic Programming
  (SLP)

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Uncertainty Management (UM) in FRIL

• Origins
• L. A. Zadeh, D. Dubis, H. Prade (1965-80s)
  Fuzzy sets, possibility theory.
• G. Shafer, P. P. Shenoy (1970s-80s)
  Depmster-Shafer theory of evidence.
• G. Klir (1970s-80s) Generalized information
  theory.
• P. Smets, J. Pearl, R.C. Jeffery (1980s-90s)
  Probabilities as degrees of belief, applications
  of probabilities in reasoning for KBS.
• B. Kosko, et. al. - Neuro-Fuzzy Computations for
  KBS.
• An unified framework (FRIL)
• J. F. Baldwin (1980s-present) Unified
  computational framework of handling propositions
  with probabilities, fuzzy logic and neural
  networks within logic programming.
• An extension (Perceptual Information Processing
  PIP)
• A. L. Ralescu A. Inoue (1997-present)
  Computational framework of handling perceptions.
  (my PhD dissertation application of text
  categorization)

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Mechanism of UM in FRIL
Extended Unification
Propositions
Predicates
Fuzzy Propositions
Classic Logic ?((query)) / tq((query)) (Symboli
c) Unification only PROLOG
Support Logic intervals (supports) of
probabilities qs((query)) Clauses with
supports Clauses containing fuzzy propositions
with supports A predicate with sigmoid and
linear combination (i.e. computation of neural
networks evidential logic) Extended rules of
combining reasoning Dempster-Shafer
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Computation of Support Logic Programming

• Canonical form of support logic
  rule((h)(f1)(fn)) ((pl pu)(nl nu))((f1))
  (sl1 su1) ((fn)) (sln sun)
• Semantics
• P(hf1fn)pl, pu P(h(f1fn))nl, nu
• B(fi)sli, sui where i1,,n
• Computation of complements
• P(hf1fn)1-pu,1-pl ( 1-P(hf1fn))
• P(h(f1fn))1-nu,1-nl ( 1-P(h(f1fn)))

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Computation of Support Logic Programming(cont.)

• Given the following in Knowledge Base
• ((h)(f1)(fn)) ((pl pu)(nl nu)) pl lt P(hf1
  fn) lt pu nl lt P(h(f1 fn)) lt nu
• ((f1)) (bl1 bu1) bl1 lt B(f1) lt bu1
• ((fn)) (bln bun) bln lt B(fn) lt bun
• How the following query is processed?
• qs((h)) B(h)?
• Computation
• Compute ((f1) (fn)) (bl bu) s.t. bl ? i
  bli, bu ? i bui(This determines the support
  pair of the hypotheses)
• Compute ((h)) (hl hu) Computation of the
  consequence
• hl plbu nl(1-bu) if pl lt nl, hl plbl
  nl(1-bl) if pl gt nl
• hu publ nu(1-bl) if pu lt nu, hu pubu
  nu(1-bu) if pu gt nu
• Note The hypotheses ((f1)(fn)) correspond to e
  from Jefferys rule

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Computation of SLP Special Cases in FRIL

• Case 1 same as qs((f1) (fn))
• ((h)(f1) (fn)) ((1 1)(0 0))
• ((fi)) (bli bui)
• qs((h)) yields ((h)) (bl bu) s.t. bl ? bli,
  bu ? bui
• Case 2 consistent with Kolmogorovs axioms
• ((h)(f1) (fn)) ((l u)(0 0))
• qs((h)) yields ((h)) (lbl ubu)
• Case 3 when P(hf1 fn) is NOT given (assumed
  to be (0 1))
• ((h)(f1) (fn)) (l u) ((l u)(0 1))
• qs((h)) yields ((h)) (lbl ubl (1-bl))
• Case 4 upper boundary of intervals (support
  pairs) is ignored.
• ((h)(f1) (fn)) ((1 1)(0 1)) is assumed.
• qs((h)) yields ((h)) (bl 1)

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Computation of SLP Rule of Combination

• How to combine multiple results?
• From rule 1 ((h)(f1) (fn)) yields ((h)) (hl1
  hu1)
• From rule 2 ((h)(g1) (gn)) yields ((h)) (hl2
  hu2)
• Obtain the intersection of support
  pairs(intervals of probabilities)
• (hl hu) (max(hl1, hl2) min(hu1, hu2))
• Error if no intersection(i.e. inconsistencies or
  contradictions on knowledge)
• Alternative Dempster-Shafer Frameworks (appeared
  later)

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Example 1 Bayesian Belief Network
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((Burglary))0.001 ((Earthquake))0.002 ((Alarm)
(general (((Burglary)(Earthquake)) ((Burglary)
(not Earthquake)) ((not Burglary)(Earthquake))
((not Burglary)(not Earthquake))) ((0.95)(0.9
4)(0.29)(0.001))))((1 1)(0 0)) ((JohnCalls)
(general (((Alarm)) ((not Alarm))) ((0.9)(0.0
5))))((1 1)(0 0)) ((MaryCalls)
(general (((Alarm)) ((not Alarm))) ((0.7)(0.0
1))))((1 1)(0 0)) qs((or (JohnCalls)(MaryCalls)
))
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General Support Logic

• General support logic rule
• ((h)(general (e1 en) ((el1 eu1) (eln eun))))
  ((1 1)(0 0))e1 (sl1 su1)..en (sln sun)
• Computation optimization
• Support pair of hypotheses (el eu) i.e. ((h))
  (el eu) in this case.
• el MIN ? eli si and
• eu MAX ? eui si subject to
• sli lt si lt sui and
• ? si 1
• Ordinary support logic rules are special cases
  consistent with above optimization.

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Example 2 Dempster-Shafer Rule of Combination
dempster fly ((fly X) (bird X)) (0.9 0.95) ((fly
X) (penguin X)) 0 ((bird X) (penguin X))
((penguin penny)) 0.4 ((bird penny)) (0.9 1)
qs((fly penny))
DSRC Switch
without
with
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Example 3 Fuzzy Pendulum Control
Fuzzy Associative Matrix (FAM) a\s P
Z N ----------------- P PB P Z Z
P Z N N Z N NB fuzzy
rules based on FAM ((move bigpos-move) (angle
pos-angle)(speed pos-speed)) ((move pos-move)
(angle pos-angle)(speed zero-speed)) ((move
zero-move) (angle pos-angle)(speed
neg-speed)) ((move pos-move) (angle
zero-angle)(speed pos-speed)) ((move zero-move)
(angle zero-angle)(speed zero-speed)) ((move
neg-move) (angle zero-angle)(speed
neg-speed)) ((move zero-move) (angle
neg-angle)(speed pos-speed))((move neg-move)
(angle neg-angle)(speed zero-speed)) ((move
bigneg-move) (angle neg-angle)(speed neg-speed))
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How to Specifically Determine move?

• FRIL generates a collection of support pairs
• ((move f1)) (sl1 su1) ((move fn)) (sln sun)
• In Example 3, n 5, i.e.bigpos_move, pos_move,
  zero_move, neg_move, bigneg_move
• We need to combine them Defuzzification
• Obtain expected fuzzy set for each support
  pair(transformation (fi, sli, sui) ?
  (expFS(fi), 1, 1))
• Combine all expected fuzzy sets(intersection
  by following the rule of combination)
• Take the expected value (COG) of the combined
  fuzzy set

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Evidential Logic in FRIL
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Example 4 Neuro-Fuzzy Pendulum Control
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(sigmoid-rule 0.50 11) ((rule1)(evlog
sigmoid-rule ((angle pos-angle) 0.5 (speed
pos-speed) 0.5))) ((rule2)(evlog sigmoid-rule
((angle zero-angle) 0.5 (speed pos-speed)
0.5))) ((rule3)(evlog sigmoid-rule ((angle
neg-angle) 0.5 (speed pos-speed)
0.5))) ((rule4)(evlog sigmoid-rule ((angle
pos-angle) 0.5 (speed zero-speed)
0.5))) ((rule5)(evlog sigmoid-rule ((angle
zero-angle) 0.5 (speed zero-speed)
0.5))) ((rule6)(evlog sigmoid-rule ((angle
neg-angle) 0.5 (speed zero-speed)
0.5))) ((rule7)(evlog sigmoid-rule ((angle
pos-angle) 0.5 (speed neg-speed)
0.5))) ((rule8)(evlog sigmoid-rule ((angle
zero-angle) 0.5 (speed neg-speed)
0.5))) ((rule9)(evlog sigmoid-rule ((angle
neg-angle) 0.5 (speed neg-speed) 0.5)))
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(sigmoid-out-bp 00 11) ((move
bigpos-move)(evlog sigmoid-out-bp ((rule1)
1.0))) (sigmoid-out-p 00 0.51) ((move
pos-move) (evlog sigmoid-out-p ((rule2) 0.5
(rule4) 0.5))) (sigmoid-out-z 00
0.331) ((move zero-move) (evlog sigmoid-out-z
((rule3) 0.33 (rule5) 0.33
(rule7) 0.34))) (sigmoid-out-n 00
0.51) ((move neg-move) (evlog sigmoid-out-n
((rule6) 0.5 (rule8)
0.5))) (sigmoid-out-bn 00 11) ((move
bigneg-move)(evlog sigmoid-out-bn ((rule9) 1.0)))
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Further Extension (call for participation)

• ((a)) high P(a)high
• ((b)(a)) (high low) P(ba)high
  and P(bnot a)low
• Fuzzy Probability probability whose number is a
  fuzzy number within 0,1.
• Approach mass assignment theoretic consider a
  fuzzy probability as a collection of supports
  with a linear combination representing a
  distribution of mass ...??
• Applications network intrusion detection,
  (video) image classification/recognition, text
  classification/categorization

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Summary

• Object-Orientation (OO) vs. Functional
  Programming Language (FPL)
• Origin of OO from AI
• OOPL may not necessarily incorporate all features
  of OO
• Many features of FPL are observed in OOPL, e.g.,
  C, JAVA
• FYI Object-Orientation vs. Logic Programming
  Language (LPL)
• Specifications of classes are given in logic
  (i.e. HC)
• Works on FRIL (I have some references)
• Uncertainty Management in LPL, i.e. FRIL
• Introduction to debate over probabilities with
  various semantics
• Use of probabilities, their intervals (supports),
  fuzzy sets, non-monotonic reasoning and
  computations of neural networks
• Unified framework underlying mass assignment
  theory

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System Integration
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Embedded FRIL

• FRIL can be embedded within applications written
  in imperative programming languages.
• C/C See the course materialshttp//penguin.ew
  u.edu/class/ai/modules.03/gameai/frilemb/frilemb.h
  tml
• JAVA See the web page at University of Bristol,
  UKhttp//www.enm.bris.ac.uk/ai/martin/downloads/J
  avaFril.html(call for students developing the
  course materials for FRIL-JAVA I/F)

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Multi Agent System with Embedded FRIL
Agent 1
Agent 2
Agent 3
Sample Application SPIDER Intrusion Detection
by multi agent approach EmoBot in Quake II
Artificial emotion engine / game AI RoboCup
Robot Soccer Game Competition (RoboLog
SWI-PROLOG, PIPOT (?) FRIL/PIP)
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PEAS

• Performance Measure
• Environment
• Actuator
• Sensor
• Example Tic-Tac-Toe
• P (getting closer to) winning the game.
• E 3x3 grid
• A place either O or X
• S game board
• How about Web-bots (IR on the Internet)?
• How about Wumpus agent?

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Wumpus World

• Performance Measure
• (Higher) score
• Environment
• 4x4 with 1 wumpus, 3 pits, 1 gold.
• Action
• move, shoot, pick
• Sensor
• stench, breeze, glitter, bump, scream

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Wumpus Solution Example

• Consider frilsrv wumpus as the game server
• Design your agent as a client to this
  server(e.g. agent ltfrilsrv hostnamegt)
• done false
• While NOT done
• Receive sensory info. (a list of words)
• If NOT killed
• Make decision of action (inference)
• Send action (a word indicating an action)
• Else done true

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In case of FRIL

• Assert sensory information addcl
• Stop if the agent is killed
• Infer the next action and send it to stdoute.g.
  ?((next-action A)(w stdout A))
• Remove asserted sensory information delclAll
  you need to define is (next-action
  A) ((next-action ..) .) They are viewed as
  production rules perceive ? act

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In case of other languages ..

• Think what State Space Representation is.
• Think which search algorithm is the most
  appropriate.
• Example
• State a collection of predicates representing
  slots that have been visited.
• Transition an action
• Given such information, you should be able to
  determine the most appropriate search algorithm.