16-Expert-SystemsChaining% • Forward%chaining%is%a data(driven%method%of%deriving%a par5cular%goal%from%agiven%knowledge%base%and%setof% inferencerules • Inference%rules%are%applied%by%matching%facts%to

COMP 4601

Expert Systems

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Mo5va5on

•  Want to capture exper5se of knowledgeable individuals in a field: – Doctors for diagnosis – Specialists for recommenda5on

•  Exper5se cannot be easily mined as few data points exist (if at all)

•  Expert system programming is dis5nc5vely different from conven5onal programming.

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Expert Systems •  Designed to func5on similar to a human expert opera5ng

within a specific problem domain

•  Used to: –  Provide an answer to a certain problem, or –  Clarify uncertain5es where normally a human expert would be

consulted

•  OOen created to operate in conjunc5on with humans working within the given problem domain, rather than as a replacement for them

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Components of an Expert System •  Knowledge Base

–  Stores knowledge used by the system, usually represented in a formal logical manner (oOen first order logic)

•  Inference System – Defines how exis5ng knowledge may be used to derive new knowledge

•  Search Control – Determines which inference to apply at a given stage of the deduc5on

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Knowledge Representa5on •  For now, we’ll use a simple If … Then … consequence rela5on

using English seman5cs

•  i.e.,: If [it is raining] Then [I should wear a coat] –  [it is raining] is the antecedent of the rela5on –  [I should wear a coat] is the consequent of the rela5on

•  Facts can be understood as consequence rela5ons with an empty antecedent –  i.e.,: “If [] Then [it is raining]” is equivalent to the fact that [it is

raining]

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Inferring New Knowledge •  New knowledge can be constructed from exis5ng knowledge

using inference rules

•  For instance, the inference rule modus ponens can be used to derive the consequent of a consequence rela5on, given that the antecedent is true

•  i.e.,: –  k1: If [it is raining] Then [I should wear a coat] –  k2: [it is raining] –  result: [I should wear a coat]

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Goal Directed Reasoning •  Inference rules are applied to knowledge base in some order

to achieve a par5cular goal

•  The goal in an expert system is formed as a ques5on, or query, to which we want the answer

•  i.e.,: [I should wear a coat]? –  note: this would read easier in English as “should I wear a coat”, but

we want to use the same proposi5onal symbol as is in our knowledge base

•  The goal of the search is to determine an answer to the query, which may be boolean as above or more complex

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Inference in rule-‐based systems

•  Two control strategies: –  forward chaining – backward chaining

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Forward Chaining •  Forward chaining is a data driven method of deriving a

par5cular goal from a given knowledge base and set of inference rules

•  Inference rules are applied by matching facts to the antecedents of consequence rela5ons in the knowledge base

•  The applica5on of inference rules results in new knowledge (from the consequents of the rela5ons matched), which is then added to the knowledge base

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Forward Chaining

•  Inference rules are successively applied to elements of the knowledge base un5l the goal is reached

•  A search control method is needed to select which element(s) of the knowledge base to apply the inference rule to at any point in the deduc5on

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Forward Chaining Example

•  Knowledge Base: –  If [X croaks and eats flies] Then [X is a frog] –  If [X chirps and sings] Then [X is a canary] –  If [X is a frog] Then [X is colored green] –  If [X is a canary] Then [X is colored yellow] –  [Fritz croaks and eats flies]

•  Goal: –  [Fritz is colored Y]?

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Forward Chaining Example Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies]

Goal [Fritz is colored Y]?

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Forward Chaining Example Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies]


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If [X croaks and eats flies] Then [X is a frog] [Fritz croaks and eats flies]

[Fritz is a frog]

Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies]


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[Fritz is a frog]

Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies] [Fritz is a frog]


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[Fritz is a frog]

?



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[Fritz is a frog]



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[Fritz is a frog] If [X is a frog] Then [X is colored green]

[Fritz is colored green]



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Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies] [Fritz is a frog] [Fritz is colored green]


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?



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[Fritz is colored green] [Fritz is colored Y] ?



Y = green

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Read the ini3al facts Begin

Filter Phase => Find the fired rules While Fired rules not empty AND not end DO

Choice Phase => Solve the conflicts Apply the chosen rule Modify (if any) the set of rules

End do End Examples: Rete algorithm, CLIPS, Jess, JEOPS, …

Forward Chaining Algorithm

Backward Chaining •  Backward chaining is a goal driven method of deriving a

par5cular goal from a given knowledge base and set of inference rules

•  Inference rules are applied by matching the goal of the search to the consequents of the rela5ons stored in the knowledge base

•  When such a rela5on is found, the antecedent of the rela5on is added to the list of goals (and not into the knowledge base, as is done in forward chaining)

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Backward Chaining

•  Search proceeds in this manner un5l a goal can be matched against a fact in the knowledge base – Remember: facts are simply consequence rela5ons with empty antecedents, so this is like adding the ‘empty goal’ to the list of goals

•  As with forward chaining, a search control method is needed to select which goals will be matched against which consequence rela5ons from the knowledge base

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Backward Chaining Example Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies] Goals [Fritz is colored Y]?

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[Fritz is colored Y]

If [X is a frog] Then [X is colored green]

[X is a frog]

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Backward Chaining Example Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies] Goals [Fritz is colored Y]? [X is a frog]



[X is a frog]

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[X is a frog]

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[X is a frog]

If [X is a canary] Then [X is colored yellow]

[X is a canary]

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Backward Chaining Example Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies] Goals [Fritz is colored Y]? [X is a frog] [X is a canary]



[X is a frog]


[X is a canary]

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[X is a frog]


[X is a canary]

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[X is a frog]


[X is a canary]

If [X croaks and eats flies] Then [X is a frog]

[X croaks and eats flies]

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Backward Chaining Example Knowledge Base If [X croaks and eats flies] Then [X is a frog] If [X chirps and sings] Then [X is a canary] If [X is a frog] Then [X is colored green] If [X is a canary] Then [X is colored yellow] [Fritz croaks and eats flies] Goals [Fritz is colored Y]? [X is a frog] [X is a canary] [X croaks and eats flies]



[X is a frog]


[X is a canary]



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[X is a frog]


[X is a canary]



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[X is a frog]


[X is a canary]


[X croaks and eats flies] [Fritz croaks and eats flies]

X = Fritz, Y = green

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[X is a frog] [X is a canary]


[X croaks and eats flies] [Fritz croaks and eats flies]

X = Fritz, Y = green

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Filter Phase IF set of selected rules is empty THEN Ask the user ELSE

WHILE not end AND we have a rule to select DO Choice Phase Add the condi5ons of the rules IF the condi5on not solved THEN put the condi5on as a goal to solve

END WHILE Examples: Prolog: SWI-‐Prolog, tuProlog, …

Backward Chaining Algorithm

Inference in rule-‐based systems: Contras5ng Forward and Backward

Chaining

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Forward & backward chaining

•  The choice of strategy depends on the nature of the problem.

•  Assume the problem is to get from facts to a goal (e.g. symptoms to a diagnosis).

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Backward chaining is the best choice if: •  The goal is given in the problem statement, or can sensibly be guessed at the beginning of the consulta5on;

or: •  The system has been built so that it some5mes asks for pieces of data (e.g. "please now do the gram test on the pa5ent's blood, and tell me the result"), rather than expec5ng all the facts to be presented to it.

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Backward chaining •  This is because (especially in the medical domain) the test may be – expensive, – or unpleasant, – or dangerous for the human par5cipant

so one would want to avoid doing such a test unless there was a good reason for it.

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Forward chaining is the best choice if: •  All the facts are provided with the problem statement;

or: •  There are many possible goals, and a smaller number of paperns of data;

or: •  There isn't any sensible way to guess what the goal is at the beginning of the consulta5on.

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•  Note also that –  a backwards-‐chaining system tends to produce a sequence of ques5ons which seems focussed and logical to the user,

–  a forward-‐chaining system tends to produce a sequence which seems random & unconnected.

•  If it is important that the system should seem to behave like a human expert, backward chaining is probably the best choice.

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•  Some systems use mixed chaining, where some of the rules are specifically used for chaining forwards, and others for chaining backwards. The strategy is for the system to chain in one direc5on, then switch to the other direc5on, so that: – the diagnosis is found with maximum efficiency;

–  the system's behaviour is perceived as "human".

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Meta-‐rules

•  Meta-‐rules are rules which alter the reasoning process: these can make a produc5on system more flexible. –  e.g., a rule which chooses a par5cular style of conflict-‐resolu5on, on the basis of data in the working memory.

–  Or a rule which switches from forward to backward chaining at a suitable moment in the reasoning process.

–  Or a rule which "decides" to consider a certain type of rule before other types.

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Problem decomposi5on into an and-‐or graph

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•  A technique for reducing a problem to a produc5on system.

•  One par5cular form of intermediate representa5on. – A structured representa5on of the knowledge, which is not yet in the form of code that can be put into an expert system’s knowledgebase.

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•  A technique for reducing a problem to a produc5on system, as follows: – The principle goal is iden5fied; it is split into two or more sub-‐goals; these, too are split up.

– A goal is something you want to achieve. A sub-‐goal is a goal that must be achieved in order for the main goal to be achieved.

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– A graph is drawn of the goal and sub-‐goals. –  Each goal is wripen in a box, called a node, with its subgoals underneath it, joined by links.

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–  The leaf nodes at the bopom of the tree -‐ the boxes at the bopom of the graph that don’t have any links below them

-‐ are the pieces of data needed to solve the problem.

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•  A goal may be split into 2 (or more) sub-‐goals, BOTH of which must be sa5sfied if the goal is to succeed; the links joining the goals are marked with a curved line, like this:

Goal 1 Goal 2 82


•  Or a goal may be split into 2 (or more) sub-‐goals, EITHER of which must be sa5sfied if the goal is to succeed; the links joining the goals aren't marked with a curved line:

Goal 1 Goal 2 83


•  Example •  "The func3on of a financial advisor is to help the user decide whether to invest in a savings account, or the stock market, or both. The recommended investment depends on the investor's income and the current amount they have saved:

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❶ Individuals with inadequate savings should always increase the amount saved as their first priority, regardless of income.

❷ Individuals with adequate savings and an adequate income should consider riskier but poten3ally more profitable investment in the stock market.

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❸ Individuals with low income who already have adequate savings may want to consider spliWng their surplus income between savings and stocks, to increase the cushion in savings while aXemp3ng to increase their income through stocks.

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❹ The adequacy of both savings and income is determined by the number of dependants an individual must support. There must be at least $3,000 in the bank for each dependant. An adequate income is a steady income, and it must supply at least $9,000 per year, plus $2,500 for each dependant."

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•  How can we turn this informa5on into an and-‐or graph?

•  Step 1: decide what the ul5mate advice that the system should provide is. It’s a statement along the lines of “The investment should be X”, where X can be any one of several things.

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•  Start to draw the graph by placing a box at the top:

Advise user: investment should be X

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•  Step 2: decide what sub-‐goals this goal can be split into. In this case, X can be one of three things: savings, stocks or a mixture. Add three sub-‐goals to the graph. Make sure the links indicate “or” rather than “and”.

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X is stocks X is savings X is mixture

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•  Steps 3a, 3b and 3c: decide what sub-‐goals each of the goals at the bopom of the graph can be split into. –  It’s only true that “X is savings” if “savings are inadequate”. That provides a subgoal under “X is savings”

–  It’s only true that “X is stocks” if “savings are adequate” and “income is adequate. That provides two subgoals under “X is stocks” joined by “and” links.

–  Similarly, there are two subgoals under “X is mixture” joined by “and” links.

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Savings are inadequate

Savings are adequate

Income is adequate


Income is inadequate

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•  The next steps (4a,4b,4c,4d & 4e) mainly involve deciding whether something’s big enough. – Step 4a: savings are only inadequate if they are smaller than a certain figure (let’s call it Y).

– Step 4b: savings are only adequate if they are bigger than this figure (Y).

– Step 4c: income is only adequate if it is bigger than a certain figure (let’s call it W), and also steady.

– Step 4d is the same as 4b. Step 4e is like 4c, but “inadequate”, “smaller” and “not steady”.

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Savings are inadequate


Income is adequate


Income is inadequate

Amount saved < Y Amount

saved > Y Income is steady

Income is not steady

Income > W

Income < W

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•  Now we need a box in which the value of Y is calculated:

and we need a box in which the value of W is calculated:

Y is Z 5mes 3000

W is 9000 plus 2500 5mes Z 96

•  Z is the number of dependants, so we need a box in which this value is obtained:

•  We can now add these last three boxes into the bopom layers of the graph in the same way as we’ve added all the others:

Client has Z dependants

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•  Pieces of evidence describing the current state of affairs appear in the bopom layer of the graph.

•  In some cases, these are statements that may or may not be true, depending on the features of the case currently under considera5on.

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•  In the next layer up, there are simple opera5ons such as calcula5ons and comparisons.

•  The lines indicate which pieces of evidence act is inputs to these opera5ons.

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•  In the upper layers, there are conclusions that can be drawn, if the pieces of evidence (and the results of the simple opera5ons) feeding into them (from below) are true.

•  Above them, there are further conclusions that can be drawn if the conclusions feeding into them are true.

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•  At the top, we have the final conclusion of the reasoning process.

•  The variables W, Y and Z allow this graph to represent both numerical and logical reasoning. The variable X allows it to deliver more than one possible conclusion.

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•  Students oOen seem to mix up this sort of chart with a flow-‐chart. It isn’t the same thing at all. • A flow-‐chart shows the sequence of opera5ons that a program must go through (probably with some branching) to execute its task.

•  The and-‐or graph shows the pieces of evidence that must be present if a certain conclusion is to be reached.

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• Why draw an and-‐or chart? •  Because it makes the point that a decision-‐making process like this can be broken down into a sequence of simple decisions, in a very systema5c way.

•  Because it’s a first step towards turning a human being’s reasoning into a collec5on of produc5on rules.

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•  The and-‐or chart can be considered as a backward-‐chaining produc5on system, reading from the top to the bopom. Or as a forward-‐chaining produc5on system, reading from the bopom to the top.

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•  Every node is the conclusion of a produc5on rule, except for the leaf nodes at the bopom, which are requests for informa5on from the user.

• When several links enter a node from below, they represent the condi5ons for that produc5on rule. They may be joined by "and" connec5ves or by "or" connec5ves.

• Alterna5vely, if several links (or groups of links) enter a node from below, and they are "or" links (or groups of links separated by "or"), this can represent several different produc5on rules which all have the same conclusion.

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Produc5on rule: if savings adequate and income adequate then X is stocks

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Produc5on rule: if income < W and income is not steady then income is inadequate

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Produc5on rule: if amount saved < Y then savings inadequate

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Produc5on rule: if X is savings or X is stocks or X is mixture then advise user investment should be X

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IMPLEMENTING AN AND-‐OR CHART IN PROLOG

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% Top level goal advise_user(X, stocks) :-‐

stocks(X). advise_user(X, mixture) :-‐

mixture(X). advise_user(X, savings) :-‐

savings(X, inadequate). savings(X, adequate) :-‐

saved(X, Y), required_savings(X, Z), Y > Z, !.

savings(_, inadequate). required_savings(X, Z) :-‐

dependents(X, Y), Z is Y * 3000.

stocks(X) :-‐ savings(X, adequate), income(X, adequate).

income(X, adequate) :-‐

income_steady(X), salary(X, W), required_income(X, W1), W > W1, !.

income(_, inadequate). required_income(X, W) :-‐

dependents(X, Z), W is 9000 + 2500 * Z.

mixture(X) :-‐

savings(X, adequate), income(X, inadequate).

% Facts for Fred. salary(fred, 4000). income_steady(fred). saved(fred, 1000). dependents(fred, 2).

Require facts for each person in

order to have the expert system work; however, you could ask ques5ons to achieve this.


•  The underlying principle is that state spaces can always be converted into produc5on systems, and vice-‐versa.

•  Searching a large produc5on system is essen5ally the same problem as searching a large state-‐space.

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Summary

•  Expert Systems encapsulate knowledge oOen derived from human experts

•  Expert system = inference engine + knowledge base + data

•  Two main modes of interference:

– Forward chaining – Backward chaining

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Documents

16-Expert-SystemsChaining% • Forward%chaining%is%a data(driven%method%of%deriving%a par5cular%goal%from%agiven%knowledge%base%and%setof% inferencerules • Inference%rules%are%applied%by%matching%facts%to