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CPECSC 481: KnowledgeBased Systems

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Title: CPECSC 481: KnowledgeBased Systems


1
CPE/CSC 481 Knowledge-Based Systems
  • Dr. Franz J. Kurfess
  • Computer Science Department
  • Cal Poly

2
Course Overview
  • Introduction
  • Knowledge Representation
  • Semantic Nets, Frames, Logic
  • Reasoning and Inference
  • Predicate Logic, Inference Methods, Resolution
  • Reasoning with Uncertainty
  • Probability, Bayesian Decision Making
  • Expert System Design
  • ES Life Cycle
  • CLIPS Overview
  • Concepts, Notation, Usage
  • Pattern Matching
  • Variables, Functions, Expressions, Constraints
  • Expert System Implementation
  • Salience, Rete Algorithm
  • Expert System Examples
  • Conclusions and Outlook

3
Overview Reasoning and Uncertainty
  • Motivation
  • Objectives
  • Sources of Uncertainty and Inexactness in
    Reasoning
  • Incorrect and Incomplete Knowledge
  • Ambiguities
  • Belief and Disbelief
  • Probability Theory
  • Bayesian Networks
  • Dempster-Shafer Theory
  • Certainty Factors
  • \Approximate Reasoning
  • Fuzzy Logic
  • Important Concepts and Terms
  • Chapter Summary

4
Logistics
  • Introductions
  • Course Materials
  • textbooks (see below)
  • lecture notes
  • PowerPoint Slides will be available on my Web
    page
  • handouts
  • Web page
  • http//www.csc.calpoly.edu/fkurfess
  • Term Project
  • Lab and Homework Assignments
  • Exams
  • Grading

5
Bridge-In
6
Pre-Test
7
Motivation
8
Objectives
9
Evaluation Criteria
10
Introductions
  • reasoning under uncertainty and with inexact
    knowledge
  • heuristics
  • ways to mimic heuristic knowledge processing
  • methods used by experts
  • empirical associations
  • experiential reasoning
  • based on limited observations
  • probabilities
  • objective (frequency counting)
  • subjective (human experience )
  • reproducibility
  • will observations deliver the same results when
    repeated

11
Dealing with Uncertainty
  • expressiveness
  • can concepts used by humans be represented
    adequately?
  • can the confidence of experts in their decisions
    be expressed?
  • comprehensibility
  • representation of uncertainty
  • utilization in reasoning methods
  • correctness
  • probabilities
  • relevance ranking
  • long inference chains
  • computational complexity
  • feasibility of calculations for practical purposes

12
Sources of Uncertainty
  • data
  • missing data, unreliable, ambiguous, imprecise
    representation, inconsistent, subjective, derived
    from defaults,
  • expert knowledge
  • inconsistency between different experts
  • plausibility
  • best guess of experts
  • quality
  • causal knowledge
  • deep understanding
  • statistical associations
  • observations
  • scope
  • only current domain?

13
Sources of Uncertainty (cont.)
  • knowledge representation
  • restricted model of the real system
  • limited expressiveness of the representation
    mechanism
  • inference process
  • deductive
  • the derived result is formally correct, but wrong
    in the real system
  • inductive
  • new conclusions are not well-founded
  • unsound reasoning methods

14
Uncertainty in Individual Rules
  • individual rules
  • errors
  • domain errors
  • representation errors
  • inappropriate application of the rules
  • likelihood of evidence
  • for each premise
  • for the conclusion
  • combination of evidence from multiple premises

15
Uncertainty and Multiple Rules
  • conflict resolution
  • if multiple rules are applicable, which one is
    selected
  • explicit priorities, provided by domain experts
  • implicit priorities derived from rule properties
  • specificity of patterns, ordering of patterns
    creation time of rules, most recent usage,
  • compatibility
  • contradictions between rules
  • subsumption
  • one rule is a more general version of another one
  • redundancy
  • missing rules
  • data fusion
  • integration of data from multiple sources

16
Basics of Probability Theory
  • mathematical approach for processing uncertain
    information
  • sample space setX x1, x2, , xn
  • collection of all possible events
  • can be discrete or continuous
  • probability number P(xi)likelihood of an event
    xi to occur
  • non-negative value in 0,1
  • total probability of the sample space is 1
  • for mutually exclusive events, the probability
    for at least one of them is the sum of their
    individual probabilities
  • experimental probability
  • based on the frequency of events
  • subjective probability
  • based on expert assessment

17
Compound Probabilities
  • describes independent events
  • do not affect each other in any way
  • joint probability of two independent events A and
    BP(A ? B) n(A ? B) / n(s) P(A) P (B)
  • where n(S) is the number of elements in S
  • union probability of two independent events A and
    BP(A ? B) P(A) P(B) - P(A ? B) P(A) P(B)
    - P(A) P (B)
  • where n(S) is the number of elements in S

18
Conditional Probabilities
  • describes dependent events
  • affect each other in some way
  • conditional probability of event a given that
    event B has already occurredP(AB) P(A ? B) /
    P(B)

19
Advantages and Problems of Probabilities
  • advantages
  • formal foundation
  • reflection of reality (a posteriori)
  • problems
  • may be inappropriate
  • the future is not always similar to the past
  • inexact or incorrect
  • especially for subjective probabilities
  • knowledge may be represented implicitly

20
Bayesian Approaches
  • derive the probability of a cause given a symptom
  • has gained importance recently due to advances in
    efficiency
  • more computational power available
  • better methods
  • especially useful in diagnostic systems
  • medicine, computer help systems
  • inverse or a posteriori probability
  • inverse to conditional probability of an earlier
    event given that a later one occurred

21
Bayes Rule for Single Event
  • single hypothesis H, single event EP(HE)
    (P(EH) P(H)) / P(E)or
  • P(HE) (P(EH) P(H) / (P(EH)
    P(H) P(E?H) P(?H) )

22
Bayes Rule for Multiple Events
  • multiple hypotheses Hi, multiple events E1, ,
    Ei, , EnP(HiE1, E2, , En) (P(E1, E2, ,
    EnHi) P(Hi)) / P(E1, E2, , En)or
  • P(HiE1, E2, , En) (P(E1Hi) P(E2Hi)
    P(EnHi) P(Hi)) / ?k P(E1Hk) P(E2Hk)
    P(EnHk) P(Hk)with independent pieces of
    evidence Ei

23
Advantages and Problems of Bayesian Reasoning
  • advantages
  • sound theoretical foundation
  • well-defined semantics for decision making
  • problems
  • requires large amounts of probability data
  • sufficient sample sizes
  • subjective evidence may not be reliable
  • independence of evidences assumption often not
    valid
  • relationship between hypothesis and evidence is
    reduced to a number
  • explanations for the user difficult
  • high computational overhead

24
Dempster-Shafer Theory
  • mathematical theory of evidence
  • notations
  • frame of discernment FD
  • power set of the set of possible conclusions
  • mass probability function m
  • assigns a value from 0,1 to every item in the
    frame of discernment
  • mass probability m(A)
  • portion of the total mass probability that is
    assigned to an element A of FD

25
Belief and Certainty
  • belief Bel(A) in a subset A
  • sum of the mass probabilities of all the proper
    subsets of A
  • likelihood that one of its members is the
    conclusion
  • plausibility Pl(A)
  • maximum belief of A
  • certainty Cer(A)
  • interval Bel(A), Pl(A)
  • expresses the range of belief

26
Combination of Mass Probabilities
  • m1 ? m2 (C) ? X ? YC m1(X) m2(Y) / 1- ?X ?
    YC m1(X) m2(Y) where X, Y are hypothesis
    subsets and C is their intersection

27
Advantages and Problems of Dempster-Shafer
  • advantages
  • clear, rigorous foundation
  • ability oto express confidence through intervals
  • certainty about certainty
  • problems
  • non-intuitive determination of mass probability
  • very high computational overhead
  • may produce counterintuitive results due to
    normalization
  • usability somewhat unclear

28
Certainty Factors
  • shares some foundations with Dempster-Shafer
    theory, but more practical
  • denotes the belief in a hypothesis H given that
    some pieces of evidence are observed
  • no statements about the belief is no evidence is
    present
  • in contrast to Bayes method

29
Belief and Disbelief
  • measure of belief
  • degree to which hypothesis H is supported by
    evidence E
  • MB(H,E) 1 IF P(H) 1 (P(HE) -
    P(H)) / (1- P(H)) otherwise
  • measure of disbelief
  • degree to which doubt in hypothesis H is
    supported by evidence E
  • MB(H,E) 1 IF P(H) 0 (P(H) -
    P(HE)) / P(H)) otherwise

30
Certainty Factor
  • certainty factor CF
  • ranges between -1 (denial of the hypothesis H)
    and 1 (confirmation of H)
  • CF (MB - MD) / (1 - min (MD, MB))
  • combining antecedent evidence
  • use of premises with less than absolute
    confidence
  • E1 ? E2 min(CF(H, E1), CF(H, E2))
  • E1 ? E2 max(CF(H, E1), CF(H, E2))
  • ?E ? CF(H, E)

31
Combining Certainty Factors
  • certainty factors that support the same
    conclusion
  • several rules can lead to the same conclusion
  • applied incrementally as new evidence becomes
    available
  • Cfrev(CFold, CFnew)
  • CFold CFnew(1 - CFold) if both gt 0
  • CFold CFnew(1 CFold) if both lt 0
  • CFold CFnew / (1 - min(CFold, CFnew)) if
    one lt 0

32
Advantages and Problems of Certainty Factors
  • Advantages
  • simple implementation
  • reasonable modeling of human experts belief
  • expression of belief and disbelief
  • successful applications for certain problem
    classes
  • evidence relatively easy to gather
  • no statistical base required
  • Problems
  • partially ad hoc approach
  • theoretical foundation through Dempster-Shafer
    theory was developed later
  • combination of non-independent evidence
    unsatisfactory
  • new knowledge may require changes in the
    certainty factors of existing knowledge
  • certainty factors can become the opposite of
    conditional probabilities for certain cases
  • not suitable for long inference chains

33
Fuzzy Logic
  • approach to a formal treatment of uncertainty
  • relies on quantifying and reasoning through
    natural language
  • uses linguistic variables to describe concepts
    with vague values
  • tall, large, small, heavy, ...

34
Get Fuzzy
35
Fuzzy Set
  • categorization of elements xi into a set S
  • described through a membership function m(s)
  • associates each element xi with a degree of
    membership in S
  • possibility measure Possx?S
  • degree to which an individual element x is a
    potential member in the fuzzy set S
  • possibility refers to allowed values
  • probability expresses expected occurrences of
    events
  • combination of multiple premises
  • Poss(A ? B) min(Poss(A),Poss(B))
  • Poss(A ? B) max(Poss(A),Poss(B))

36
Fuzzy Set Example
membership
tall
short
medium
1
0.5
height (cm)
0
0
50
100
150
200
250
37
Fuzzy vs. Crisp Set
membership
tall
short
medium
1
0.5
height (cm)
0
0
50
100
150
200
250
38
Fuzzy Inference Methods
  • how to combine evidence across rules
  • Poss(BA) min(1, (1 - Poss(A) Poss(B)))
  • implication according to Max-Min inference
  • also Max-Product inference and other rules
  • formal foundation through Lukasiewicz logic
  • extension of binary logic to infinite-valued logic

39
Example Fuzzy Reasoning
40
Advantages and Problems of Fuzzy Logic
  • advantages
  • general theory of uncertainty
  • wide applicability, many practical applications
  • natural use of vague and imprecise concepts
  • helpful for commonsense reasoning, explanation
  • problems
  • membership functions can be difficult to find
  • multiple ways for combining evidence
  • problems with long inference chains

41
Post-Test
42
Evaluation
  • Criteria

43
Use of References
  • Giarratano Riley 1998
  • Russell Norvig 1995
  • Jackson 1999
  • Durkin 1994

Giarratano Riley 1998
44
Important Concepts and Terms
  • natural language processing
  • neural network
  • predicate logic
  • propositional logic
  • rational agent
  • rationality
  • Turing test
  • agent
  • automated reasoning
  • belief network
  • cognitive science
  • computer science
  • hidden Markov model
  • intelligence
  • knowledge representation
  • linguistics
  • Lisp
  • logic
  • machine learning
  • microworlds

45
Summary Chapter-Topic
46
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