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CS621: Artificial Intelligence
Pushpak Bhattacharyya
CSE Dept.,
IIT Bombay
Lecture–2: Introduction: Search+Logic
Logistics
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Faculty instructor: Dr. Pushpak Bhattacharyya
(www.cse.iitb.ac.in/~pb)
TAs: Saurabh (saurabhsohoney@cse), Anup
(anup@cse)
Course home page
 www.cse.iitb.ac.in/~cs621-2009
 Lectures mirrored at
www.cse.iitb.ac.in/~pb/cs621-2009
Venue: CSE Building: S9
1 hour lectures 3 times a week: Mon-9.30, Tue10.30, Thu-11.30
Disciplines which form the core of AI- inner circle
Fields which draw from these disciplines- outer circle.
Robotics
NLP
Expert
Systems
Search,
Reasoning,
Learning
KnowledgeRepresentation
Planning
Computer
Vision
Search: Everywhere
Planning
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(a) which block to pick, (b) which to stack, (c) which to unstack, (d)
whether to stack a block or (e) whether to unstack an already stacked
block. These options have to be searched in order to arrive at the right
sequence of actions.
A
B
Table
C
C
B
A
Vision
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A search needs to be carried out to find which point in the image of L
corresponds to which point in R. Naively carried out, this can become
an O(n2) process where n is the number of points in the retinal
images.
R
L
Two eye
system
World
Robot Path Planning
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searching amongst the options of moving Left, Right, Up or Down.
Additionally, each movement has an associated cost representing the
relative difficulty of each movement. The search then will have to find
the optimal, i.e., the least cost path.
R
O2
Robot
Path
O1
D
Natural Language Processing
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search among many combinations of parts of speech on the way to
deciphering the meaning. This applies to every level of processingsyntax, semantics, pragmatics and discourse.
The
Noun
man
would
like
to
play.
PrepositionVerb Noun
Verb
Verb
Expert Systems
Search among rules, many of which can apply to a
situation:
If-conditions
the infection is primary-bacteremia
AND the site of the culture is one of the sterile sites
AND the suspected portal of entry is the gastrointestinal tract
THEN
there is suggestive evidence (0.7) that infection is bacteroid
(from MYCIN)
Search building blocks
State Space : Graph of states (Express constraints
and parameters of the problem)
 Operators : Transformations applied to the states.
 Start state : S (Search starts from here)
0
 Goal state : {G} - Search terminates here.
 Cost : Effort involved in using an operator.
 Optimal path : Least cost path
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Examples
Problem 1 : 8 – puzzle
4
3
6
1
2
3
2
1
8
4
5
6
5
7
8
7
S
G
Tile movement represented as the movement of the blank space.
Operators:
L : Blank moves left
R : Blank moves right
U : Blank moves up
C(L) = C(R) = C(U) = C(D) = 1
D : Blank moves down
Problem 2: Missionaries and Cannibals
R
boat
River
boat
L
Missionaries
Missionaries
Cannibals
Cannibals
Constraints
 The boat can carry at most 2 people
 On no bank should the cannibals outnumber the missionaries
State : <#M, #C, P>
#M = Number of missionaries on bank L
#C = Number of cannibals on bank L
P = Position of the boat
S0 = <3, 3, L>
G = < 0, 0, R >
Operations
M2 = Two missionaries take boat
M1 = One missionary takes boat
C2 = Two cannibals take boat
C1 = One cannibal takes boat
MC = One missionary and one cannibal takes boat
<3,3,L>
C2
<3,1,R>
MC
<2,2,R>
<3,3,L>
Partial search
tree
Problem 3
B
B
B
W
W
W
G: States where no B is to the left of any W
Operators:
1) A tile jumps over another tile into a blank tile with cost
2
2) A tile translates into a blank space with cost 1
All the three problems mentioned
above are to be solved using A*
Power of Logic
Disciplines which form the core of AI- inner circle
Fields which draw from these disciplines- outer circle.
Robotics
NLP
Expert
Systems
Search,
Reasoning,
Learning
KnowledgeRepresentation
Planning
Computer
Vision
Circuit Verification
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Does the circuit meet the specs?
Are there faults?
are they locatable?
Example : 2-bit full adder
C1
X2
X1
Y
C2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
X1, X2: inputs; C1: prev. carry; C2: next carry; Y: output
K-Map
Y
c1
x2x1
00
01
11
10
0
0
1
0
1
1
1
0
1
0
Y  C1( X 1  X 2)  C1( X 1  X 2)
 (C1  ( X 1  X 2))
K-Map (contd..)
C2
c1
x2x1
00
01
11
10
0
0
0
1
0
1
0
1
1
1
C 2  X 2 X 1  C1( X 1  X 2)
Circuit
Verification
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First task (most difficult)
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Building blocks : predicates
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Circuit observation : Assertion on terminals
Predicates & Functions
Function–1
signal(t)
t is a terminal ; signal
takes the value 0 or 1
Function–2
type(x)
x is a circuit element;
type(x) takes the value
AND, OR, NOT, XOR
Predicate – 3
connected(t1,t2)
t1 is an output terminal
and t2 is an input
terminal
Function-3
In(n,x)
nth input of ckt element x
Function-4
Out(x)
Output of ckt element x
Alternate Full Adder Circuit
Functions
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type(X) : takes values AND, OR NOT and XOR, where X is
a gate.
in(n, X) : the value of signal at the nth input of gate X.
out(X) : output of gate X.
signal(t) : state at terminal t = 1/0
Predicates
• connected(t1,t2): true, if terminal t1 and t2 are
connected
General Properties
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Commutativity:
∀t1,t2 [connected(t1,t2) → connected(t2,t1)]
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By definition of connection:
∀t1,t2 [connected(t1,t2) → { signal(t1) =
signal(t1)}]
Gate properties
1.
OR definition:
X [{type(X)  OR} 
{(out(X)  1)  y (in(y, X)  1)}]
2.
AND definition:
X [{type(X)  AND} 
{(out(X)  1)  y (in(y, X)  1)}]
Gate properties contd…
1.
XOR definition:
X [{type(X)  XOR} 
{(out(X)  1)  (in(1, X)  in(2, X))}]
2.
NOT definition:
X [{type(X)  NOT} 
{out(X)  in(1, X)}  (no_of_inpu t(X)  1)]
Some necessary functions
a.
b.
no_of_input(x), takes values from N.
Count_ls(x), returns #1s in the input
of X
X [{type(X)  XOR} 
{(out(X)  1)  odd((count _ls(X))}]
Circuit specific properties
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Connectivity:
connected(x1, in(1,A1)),
connected(x2, in(2, A1)),
connected(out(A1), in(1, A2)) ,
connected(c1, in(2, A2)),
connected(y, out(A2)) …
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Circuit elements:
type(A1) = XOR,
type(A2) = XOR,
type(A3) = AND …
Topics to be covered (1/2)
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Search
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Logic
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General Graph Search, A*
Iterative Deepening, α-β pruning, probabilistic
methods
Formal System
Propositional Calculus, Predicate Calculus
Knowledge Representation
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Predicate calculus, Semantic Net, Frame
Script, Conceptual Dependency, Uncertainty
Topics to be covered (2/2)
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Neural Networks: Perceptrons, Back Propagation, Self
Organization
IR and AI
Semantic Web and Agents
Statistical Methods
 Markov Processes and Random Fields
 Computer Vision, NLP, Machine Learning
Planning: Robotic Systems
Confluence of NLP and CV: text and image based
search
Anthropomorphic Computing: Computational
Humour, Computational Music
Resources
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Main Text:
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Other Main References:
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Principles of AI - Nilsson
AI - Rich & Knight
Knowledge Based Systems – Mark Stefik
Journals
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Artificial Intelligence: A Modern Approach by Russell & Norvik,
Pearson, 2003.
AI, AI Magazine, IEEE Expert,
Area Specific Journals e.g, Computational Linguistics
Conferences
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IJCAI, AAAI
Allied Disciplines
Philosophy
Maths
Knowledge Rep., Logic, Foundation of
AI (is AI possible?)
Search, Analysis of search algos, logic
Economics
Expert Systems, Decision Theory,
Principles of Rational Behavior
Psychology
Behavioristic insights into AI programs
Brain Science
Learning, Neural Nets
Physics
Learning, Information Theory & AI,
Entropy, Robotics
Computer Sc. & Engg. Systems for AI
Evaluation
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(i) Exams
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(ii) Study
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Midsem
Endsem
Class test
Seminar
(iii) Work
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Assignments