CSNB234 ARTIFICIAL INTELLIGENCE Chapter 8.2 Certainty Factors (CF) Instructor: Alicia Tang Y. C. UNIVERSITI TENAGA NASIONAL

Uncertainty: Introduction In Expert Systems, we must often attempt to draw correct conclusions from poorly formed and uncertain evidence using unsound inference rules. This is not an impossible task; we do it successfully in almost every aspect of our daily survival. UNIVERSITI TENAGA NASIONAL

Uncertainty: Introduction Doctors deliver correct medical treatment for ambiguous symptoms; we understand natural language statements that are incomplete or ambiguous and so on. One of the characteristics of information available to human experts is its imperfection Information can be incomplete, inconsistent, uncertain However, we are good at drawing valid conclusion from such information UNIVERSITI TENAGA NASIONAL

So, how to define the term “Uncertainty”? Uncertainty can be defined as the lack of the exact knowledge that would enable us to reach a perfectly reliable conclusion. This is because information available to us can be in its imperfect, such as inconsistent, incomplete, or unsure, or all three. An example: unknown data or imprecise language UNIVERSITI TENAGA NASIONAL

There are many approaches to representing uncertainty in AI. UNIVERSITI TENAGA NASIONAL

Uncertainty Handling Methods E.g. Suppose: If x is a bird then x flies Abductive reasoning would say that “All fly things are birds” By property inheritance “All birds can fly” but, remember the case that Penguin cannot fly? Abductive reasoning Property inheritance Fuzzy logic Certainty Factor (CF) Bayes theorem Dempster-Shafer theory UNIVERSITI TENAGA NASIONAL

Evaluation Criteria for uncertainty handling methods Expressive power Logical correctness Computational efficiency of inference UNIVERSITI TENAGA NASIONAL

Scheme used by expert system in Handling Uncertainty MYCIN uses Certainty Factor The CF can be used to rank hypotheses in order of importance. For example if a patient has certain symptoms that suggest several possible diseases, then the disease with the higher CF would be the one that is first investigated. REVEAL uses Fuzzy logic PROSPECTOR uses Bayes theorem UNIVERSITI TENAGA NASIONAL

Purpose Design element semantics, and Formulas Certainty Factors Purpose Design element semantics, and Formulas

UNIVERSITI TENAGA NASIONAL Certainty Factor (CF) When experts put together the rule base they must agree on a CF to go with each rule. This CF reflects their confidence in the rule’s reliability. Certainty measures may be adjusted to tune the system’s overall performance, although slight variations in this confidence measure tend to have little effect on the overall running of the system. UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL Certainty Factor Certainty factors measure the confidence that is placed on a conclusion based on the evidence known so far. A certainty factor is the difference between the following two components : CF = MB[h:e] - MD[h:e] A positive CF means the evidence supports the hypothesis since MB > MD. UNIVERSITI TENAGA NASIONAL

Certainty Factor Computation CF[h:e] = MB[h:e] - MD[h:e] …………………… (I) CF[h:e] is the certainty of a hypothesis h given the evidence e. MB[h:e] is the measure of belief in h given e. MD[h:e] is the measure of disbelief in h given e. CFs can range from -1 (completely false) to +1 (completely true) with fractional values in between, and zero representing ignorance. MDs and MBs can range between 0 to 1 only. 1 - 0 0 - 1 UNIVERSITI TENAGA NASIONAL

More equations for CF computation use MB(P1 AND P2) = MIN(MB(P1), MB(P2)) ……. (II) MB(P1 OR P2) = MAX(MB(P1), MB(P2)) ……… (III) the MB in the negation of a fact can be derived as: MB(NOT P1) = 1 - MB(P1) ………………………. (IV) UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL Each rule can have an credibility (attenuation) A number from 0 to 1 which indicates its reliability. The credibility is then multiplied by the MB for the conclusion of the rule. MB(Conclusion) = MB(conditions) * credibility ….. (V) & MB[h:e1,e2] = MB[h:e1] + MB[h:e2] * (1-MB[h:e1]) …….. (VI) Credibility for each rule The goal of a rule UNIVERSITI TENAGA NASIONAL

A CF Calculation Example Rule 1 IF X drives a Myvi AND X reads the Berita Harian THEN X will vote Barisan Nasional Rule 2 IF X loves the setia song OR X supports Vision 2020 Rule 3 IF X uses unleaded petrol OR X does not support Vision 2020 THEN X will not vote Barisan Nasional The set of 3 rules For deducing The chances of “KL People will vote for BN” UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL Let us assume that the individual MBs for the Conditions are as follows: X drives a Myvi car 0.9 X reads the Utusan Malaysia 0.7 X loves the 1Malaysia song 0.8 X supports Vision 2020 0.6 X uses unleaded petrol 0.7 UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL While the credibility of each rule is as follows: Rule 1 0.7 Rule 2 0.8 Rule 3 0.6 UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL The hypothesis (i.e. we want to test this) To determine: CF[ X votes BN: Rule 1, Rule 2, Rule 3 ] Rule1 and Rule2 give the MB in the proposition “X votes BN” : MB[X votes BN: Rule 1] = MIN (0.9, 0.7) * 0.7 = 0.49 -- using II and V MB[X votes BN: Rule 2] = MAX (0.8, 0.6) * 0.8 = 0.64 -- using III and V MB[X votes BN: Rule 3] = MAX (0.7), (1-0.6)) * 0.6 = 0.42 -- using II, IV and V UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL Combining the Rule 1 and Rule 2: MB[X votes BN: Rule1, Rule2] = MB[X votes BN: Rule1] + MB[X votes BN: Rule2] * ( 1 - MB[X votes BN: Rule 1] ) ---- using (VI) = 0.49 + 0.64 * (1 - 0.49) = 0.82 Combining the three rules: CF[ X votes BN: Rule 1, Rule 2, Rule 3 ] = MB[X votes BN: Rule 1, Rule 2] - MD[X votes BN: Rule 3] = 0.82 - 0.42 = 0.4 I disbelieve you will note I believe you won’t vote After we obtain the CF for the hypothesis, what do you think is the answer for the question: “Will someone in KL vote for BN party”? UNIVERSITI TENAGA NASIONAL

In an expert system that implements “uncertainty handling” The answer is “May be” (and not a “yes” or a “no”) Isn’t it exactly the way you and I say it! Certainty Factor has been criticised to be excessively ad-hoc. The semantic of the certainty value can be subjective and relative. But the human expert’s confidence in his reasoning is also approximate, heuristic and informal UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL Advantages of CF scheme: a simple computational model that permits experts to estimate their confidence in conclusion it permits the expressions of belief and disbelief in each hypothesis (expression of multiple sources of evidence is thus allowed) gathering the value of CF is easier than those in other methods UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL Bayesian Approach (I) Bayesian approach (or Bayes theorem) is based on formal probability theory. It provides a way of computing the probability of a hypothesis (without sampling) following from a particular piece of evidence, given only the probabilities with which the evidence follows from actual cause. To use this approach, reliable statistical data that define the prior probabilities for each hypothesis must be available As these requirements are rarely satisfied on real-world problem, so only a few systems have been built based on bayesian reasoning UNIVERSITI TENAGA NASIONAL

Bayesian approach (II) p(E | Hi) * p(Hi) p(Hi | E) = ------------------------------ n  p(E | Hk) * p(Hk) k= 1 evidence hypothesis Here, as you can see, a number of assumptions (i.e. independence of evidence) which cannot be made for many applications (such as in medical cases). UNIVERSITI TENAGA NASIONAL

Bayes theorem (III) where: You will get an A if you study every night for one week before exam where: p(Hi | E) is the probability that Hi is true given evidence E. p(Hi) is the probability that Hi is true overall. p(E | Hi) is the probability of observing evidence E when Hi is true. n is the number of possible hypotheses. Those who obtained an ‘A’ and they indeed studied every night before exam If there are not many cases of success of people who obtained an ‘A’ by studying hard then your chances of getting an ‘A’ by ‘hardworking’ is also lower! UNIVERSITI TENAGA NASIONAL

UNIVERSITI TENAGA NASIONAL Advantages: Most significant is their sound theoretical foundation in probability theory. Most mature uncertainty reasoning methods Well defined semantics for decision making Main disadvantage: They require a significant amount of probability data to construct a knowledge base. UNIVERSITI TENAGA NASIONAL

Dempster-Shafer theory (1967, Arthur Shafer) This theory was designed as a mathematical theory of evidence where a value between 0 and 1 is assigned to some fact as its degree of support. Similar to Bayesian method but is more general. As the belief in a fact and its negation need not sum to one ‘1’. Both values can be zero (reflecting that no information is available to make a judgment) UNIVERSITI TENAGA NASIONAL

Dempster-Shafer theory It has a belief function, Bel(x) Belief function measures the likelihood that the evidence support x. It is also used to compute the probability that the evidence supports a proposition. UNIVERSITI TENAGA NASIONAL

Reasoning from first principles It is normally supported by having a system’s structural and behavioral properties described declaratively. Model-based diagnosis is an example of system that reasons from first principle. UNIVERSITI TENAGA NASIONAL