Production Rules

7/30/2019 Production Rules

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PRODUCTION SYSTEMS

Production systems (ps) Provide a scheme for

structuring AI programs and performing the search

process.A PS consists of

A collection of condition action pairs called

production rules A database of state information

A procedure for invoking the production rules


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A PS is a model for solving an AI

problem Typical PS s

Expert system shells

which provide environmentsfor the construction of

knowledge based ES

General problem solving

architectures for problem

solving (SOAR)


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SIMPLE EXAMPLE OF A

PRODUCTION SYSTEMAccept an integer x and produce its roman numeral

representation

1. PRODUCTION RULES(a) If x is null then prompt the user and read x.

(b) If x is not null and is bigger than 39 then

print too big and make x null.(c) If x is not null and is between 10 and 39

then print x and reduce x by 10.


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(d) If x is not null and is equal to 9 then print IXand reduce x to 0.

(e) If x is not null and is between 5 and 8 then print V and reduce x by 5.

(f) If x is not null and is equal to 4 then print IV

and reduce x to 0.(g) If x is not null and is between 1 and 3 then print

I and reduce x by 1.

(h) If x is not null and is equal to 0 then print an end

of line and make x null.


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2. Database : The value of the sole variable x

3. Control Scheme : Test conditions in an

arbitrary order until one is true; execute

corresponding action; repeat indefinitely.


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;Lisp program to convert integer to Roman numerals

(Defun Roman (x))

loop

(cond

((null x)(print enter number)(setq x (read)))

(greaterp x 39) (print too big)(setq x wil))

((greaterp x 9) (print x)(setq x (diference x 10)))

((equal x 9) print ix)(setq x 0)

((greaterp x 4) (print v)(setq x (diference x 5)))

((equal x 4) print iv)(setq x 0)

((greaterp x 0) (print I) (setqx (sub1 x )))

((zerop x) (setq x nil )

)

(Go loop))


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CONTROL STRATEGIES

Whether the problem is solved or not, how

quickly the solution is arrived depends on

the control strategy. If more than one rulematches the left side of the current state,

which one to choose ?


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Requirements of a good control strategy

- IT Must Cause MotionControl strategies that do not cause motion

will never lead to a solution.

Example : In the water jug problem thestrategy of choosing the first applicable rule

from the top of the list of rules would

continuously fill the 4-gallon jug. It wouldnever solve the problem.


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- Control strategy must be systematic

Example : In the water jug problem,choosing a rule at random from among the

applicable rules causes motion, but same

state may be arrived several times, thusmany steps are needed than necessary.

A systematic Control Strategy causes global

as well as local motion


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Two systematic control strategies

1. Depth-first search

2. Breadth-first search

Depth-first search - Method :

Construct a tree with initial state as root

Generate its offspring

Pursue the branch until it yields a solution or it is

a dead end i.e. no child can be generated If a dead end is reached, back tracking occurs, i.e.the most recently visited state is expanded andnodes are revisited


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ALGORITHM : DFS1. If the initial state is a goal stats quit

and return success.

2. Otherwise do the following untilsuccess or failure is signaled.

(a) Generate a successor E of the initialstate. If there are no more successors,

signal failure.

(b) Call DFS with E as the initial state

(c) If success is returned,signal success otherwise continuein this loop.

A depth first search tree (DFS) for water jug problem.


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BREADTHFIRST SEARCHMETHOD :

Construct a tree with initial state (IS) as root

Generate offsprings by applying each of the

applicable rules to IS

For each leaf node generate its successors

Continue the process until some ruleproduces the goal state


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ALGORITHM (BFS)

1. Create a variable called node-listand set it to initial state.

2. Until a goal state is found or

node-list is empty do(a) Remove the first element from

node-list and call it E.

If node-list was empty quit.

(b) For each way that each rule

can match E, do : Two Levels of BFS for water jug problem

(i) Apply the rule to generate a new state

(ii) If the new state is a goal state, quit and return this state.

(iii) Otherwise, add the new-state to the end of node-list


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Example : Consider a map of cities ofFrance, Transformed into a graph, which is

an explicit representation of a state space.

The implicit state space would be generated

by applying the operators rather than pre-

existing.


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(defun extract-path (n)

(cond ((null n) nil)

(t (append (extract-path (get n pointer))

(list n ) )) ) )

defun successors (N) (GET N ADJCNT)

(defun ((null L1 L2)

(cond ((Null L1) nil )

(( MEMBER (CAR (CDR L1 L2))

(( T cons (car L1) (set-diff (cdr L1) L2)))))

for bfs step 5 i.e. (setq L (set-diff L closed))

(setq open (append L (set-diff open L))) is replaced with(setq L (set-diff(set-diff L open) closed))

(setq open (append open L ))

(new nodes are put on the end of open)


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Adjacency data (For eachcity, the other citiesdirectly, connected to it)

(putprop brest (rennes)adhct)

(putrop rennes (laen parisbrist

nantes) adjct)

(putprop paris (Calais nancy)

Dijon limoges rennes

Caen) adjct :Depth-first-search remes

aviiur)

Given the round about route(rennes caen, calajs nancystrasdooy Dijon lyongrendble avignon)


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BFS DFS

1. Never gets trapped exploring a path May explore a single un-

which does not lead to a solution. fruitful path for a long time.

2. Guaranteed to find a solution if it May find a long path

exits. If multiple solutions exists a when a shorter path exists

minimal one will be found

3. Requires more memory Requires lessmemory

(All the tree that has so far been (Only the nodes on the

visited must be stored) current path are to

be stored)

4. All nodes in level n must be By chance a solution may be

examined before any node found without examiningmuch

on level n + 1 can be of the nodes

examined

5. Only the best solution is found Can stop when any one

solution is found


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THE TRAVELLING

SALESPERSON PROBLEM A list of cities a sales persons has to visit

exactly once.

Direct routs between each pair of cities.

The salesperson has to start at any one of

the cities and make a round trip .

Find the shortest route


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The number of paths among N different cities is

N-1, N-2, 3.2.1 = (N-1) !

The time to examine a single path is proportional

to N The total tine to perform the search is proportional

to N !

If N = 10, 10! =3, 625, 800If N = 25, the number will be very large

This phenomenon is called combinatorial explosion


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BRANCH AND BOUND TECHNIQUE

Generate complete paths keeping track of

the shorted path found so far

Stop exploring any path, as soon as itspartial length exceeds the shortest path

found so far

The method is efficient but still requiresexponential time.


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HEURISTIC SEARCH Control strategy to solve hard problems efficiently

Need not cause motion and need not be systematicbut provides a very good solution; the solution

may not be the best A heuristic is a rule of thumb or judgementaltechnique used in problem solving

Heuristic methods lead to a solution some of the

time but provide no guarantee of success They reduce the number of a alternatives, and

thereby obtain a solution in a tolerable amount oftime


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SOLUTION OF TRAVELLING

SALESPERSON PROBLEM

USING HEURISTIC SEARCH

1. Arbitrarily select a start city

2. To select the next city, look at all citiesnot yet visited and select the one closest tothe current city, go to it next

Repeat step2 until all cities have beenvisited

Execution time = 1+2+3+ . +(N-1)+N =N(N+1)/2 = 0(N2)


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Some special purpose heuristicsProblem :Discovering interesting ideasconsider a function

Y = f ( x , y) = x + yHeuristic : Two arguments are identicalleads to the idea of squaring

Y = f (x, y) = x U y

The heuristic leads to the idea of identifyfunction


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REASONS FOR USING HEURISTICS

Without heuristics we end up in a combinatorial explosion

Rarely we need the optimum solution; a goodapproximation usually serves well.

People when they solve problems are not optimizers butsatisfiers. As soon as they find a good solution, they quit

Example : Searching for a parking space

The approximations produced by heuristics may not be

very good in the worst case, worst cases rarely arise in thereal world.


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In a rule based search process, heuristic

knowledge can be incorporated In the rules

themselves as in a chess playing system not simply the set of

legal moves, but a set of sensible moves

determined by the rule writer may be described.

As a heuristic function that evaluates problem

states and determines how desirable they are. The

heuristic function is evaluated to a number.


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PROBLEM

CHARACTERISTICSHeuristic Search is a general method to

solve a large class of problems. To choose a

specific appropriate method for a problem,it is necessary to analyse the problem along

several key dimensions.

1. Is the problem decomposable into a set ofindependent smaller or easier sub-

problems?


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Example of a decomposable problem


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Example of a non-decomposable problem

Consider the BLOCKS WORLD problem


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Available operators:

1. If block x has nothing on it, pick up x and put

it on table

CLEAR (x) ON (x, TABLE)2. CLEAR (x) and CLEAR (y) ON (x,y)

The goal state can be represented as ON(B,C)

and ON(A,B)

To achieve ON(B,C) from start state we can

apply ON (C,TABLE) and ON(B,C)


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contd..


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contd..

While achieving the second sub-goal, the

first sub-goal is not achieved, as the two

sub-problems are not independent.They interact and these interactions must

be considered in order to arrive at a solution

for the entire problem.


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2.Can solution steps be ignored or undone?

Mathematical theorem proving :

- Suppose we prove a lemma, but it is not useful

- We prove another lemma which is useful toprove the theorem

- We didn't lose anything except some effort

- Simple control strategy to solve the problem


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Can solution steps be ignored or undone? Contd..

suppose we slide 5 into empty cell.

To slide 6 into the empty cell, we need to undo the

previous step.To undo an incorrect step, you need to record the

order in which operations are performed.

Mistakes can be recovered but not easily.

Slightly more complicated control strategy


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Can solution steps be ignored or undone? Contd..

Problem of playing chess

A great deal of effort for making each decision

A stupid move realized after a couple of movescannot be corrected.

Cannot play as though it had never made astupid move

Ignorable problemssolution steps can be ignored

Recoverable problems solution steps can be

undoneIrrecoverable problems solution steps cannot beundone


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3. Is the Universe predictable ?

8 Puzzle problem : A certain outcome problemis one in which we can plan a sequence of movesto reach a resulting state

Planning can be used to generate a sequence ofoperations that guarantee to lead to a solution

Playing Bridge is an uncertain outcome problem Cannot exactly know where all the cards are and

what the other player will do on his turn


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Probabilities of various outcomes are used tochoose a plan

Planning can generate a sequence of operators

with a good probability of leading to a solution. A number of solution paths have to be explored

Hardest problems -Irrecoverable, uncertain outcome

Other examples : controlling a robot arm

- Obstacles into the path

- Gears might stick

-Error may cause the arm to knock over astack of things

Helping a lawyer decide how to defend his clientagainst murder case.


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4. Is a good solution absolute or relative ?

Consider the following database of facts

1. Marcus was a man

2. Marcus was a Pompeian

3. Marcus was born in 40 A.D

4. All men are mortal5. All Pompeian's died when the volcano erupted

in 79 A.D

6. No mortal lives longer than 150 years

7. It is now 2003 A.D


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Consider the question Is Marcus alive?

There are two reasoning paths leading to theanswerMarcus is dead.

Path1 Axioms used

8. Marcus is mortal 1,4

9. Marcuss age is 1963 years 3,7

10.Marcus is dead 8,9,6

Reasoning path- 2

11.All Pompeian's are dead now 7,5

12.Marcus is dead 11,2


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Comments :

We are interested in only the answer to

the question

- it does not matter which path we

follow

If one path leads successfully to the

answer, there is no need of exploring the

other path


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Now consider the following table of distances

(Km) for traveling sales person problem :

New Delhi Bombay Madras Calcutta

New Delhi - 2200 2350 2800

Bombay 2200 - 3000 2500Madras 2350 3000 - 1200

Calcutta 2800 2500 1200 -

Th l i t fi d th h t t th th t i it


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The goal is to find the shortest path that visits

each city exactly once.

First Path is not definitely the solution. This example

illustrates any-path problem or best-path problem.


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5. Is the solution a state or a path to a state?

consider the sentence The bank president

ate a dish of pasta salad with the fork.

In interpreting the sentence, some of thesources of ambiguity are


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Is the solution a state or a path to a state?

Contd..


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Contd..

PASTA SALAD SALAD contains pasta or not? Dogfood does not contain dog

With the fork modifies the verb eat;

He ate with vegetables or He ate with friends, thenstructure would be different.

Thus search would be required for complete

interpretation for the sentence.For the above NLU problem, no need to record the

processing by which the interpretation was found.


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Contd..

In the water jug problem, it is not sufficient

to say that the final state is (2,0), but the

path or a sequence of operations leading tothe goal state are required .

NLU problem- solution is a state

Water jug problempath to a state


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6. What is the role of knowledge ?

Playing Chess requires rules for determining the legalmoves and control mechanism to implement search.

Additional knowledge as good strategy and tactics help

to constrain the search and speed up the execution.Consider the problem of scanning daily newspapers and todecide which paper supports which party.

- For this problem, a great deal of knowledge as namesof candidates in each party, opposing government meanssupporting opposition party etc. is required.


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7. Does the task require interaction with a

person?

Does the task require interaction with a person?

Theorem proving is a solitary problem. : The

program is capable of finding a proof withoutinteraction

Expert system is a conversational problem

.Communication is required either to provide

additional assistance to computer or to provideadditional information to the user.


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Types of Productive (PS) systems

Monotonic production system :

The application of a rule prevents the

application of another rule that could alsohave been applied at the time the first rule

was selected. A PS which is not monotonic

is called non monotonic.


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Partially commutation (PS) :

It is a PS with the property if the sequence of rulestransforms state x into state y, then anypermutation of these rules also transforms state xinto state y.

A commutative PS is one that is monotonic andpartially commutative. Formally all kinds ofproblems can be solved by all kinds of system.Practically there is a relationship between thekinds of problems and kinds of systems.


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Examples :

Monotonic No monotonic

Partiallycommutative

Theoremproving

Robotnavigation

blocks word

8-puzzle

Not Partiallycommutative

Chemicalsynthesis

Bridge


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Monotonic & partially commutative systems arefor ignorable problems

Non Monotonic & partially commutative systemsare for recoverable problems.

Issues in the design of search problems :

Search process can be viewed as a traversal oftree.Each node represents a problem state andeach arc represents a relationship between thestates.

In practice, most of the tree need not be exploredfor reaching a solution.

Most search programs represent the tree implicitlyin the rules and generate explicitly those parts

that they decide to explore.


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Issues in search technique :

The direction in which to conduct the test

forward versus backward reasoning (to search

from start state to goal state or from goal to start)

How to select applicable rules or how to match

rules against states How to represent each node of the search process

(knowledge representation problem).

The search space may be an arbitrary directed

graph rather than a tree as same nodes may be

generated as part of several paths.


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Search trees versus search graphs


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Search trees versus search graphs contd..

Using tree search requires no book keeping

but lot of effort is wasted in expanding the same

nodes.

By traversing a directed graph, the waste of effort

can be avoided with additional book keeping. BFS

keeps track of nodes generated, but DFS does not

DFS could be modified with the expense ofadditional storage.


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Algorithm to search duplicate

nodes in search graph1. Examine the set of nodes generated to see if

the new node already exists.

2. If it does not, add it to the graph

3. If it does already exists, do the following :a) Set the node being expanded to point to

the already existing node.

b) If the new path is better than the oldpath, record the new path and propagate

the change.

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Production Rules