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eductions. Constraint satisfaction techniques, being an emerging research area, will be presented in detail in chapter 19. Means and ends analysis and problem reduction techniques, on the other hand, are available in most text books [7] and we omit these for lack of space. Exercises 1. Using the Euclidean distance of a node (x, y) from a fixed node (2, 2), i.e., h = [ (x –2) 2 + (y –2) 2 1 / 2 ] solve the water-jug problem by paper and pencil by A* algorithm. Does this heuristic function return an optimal path? Consequently, can you call it an admissible heuristic? 2. The 8-puzzle problem is similar to the 4-puzzle problem we discussed in chapter 1. The only difference is that there exist 9 cells and 8 tiles instead of the 4 cells and 3 tiles of a 4-puzzle problem. Can you select a heuristic function for the 8-puzzle problem? Solve the 8-puzzle problem by the A* algorithm with your selected heuristic function. 3. Show the computation for the first 3 ply moves in a tac-tac-toe game using the α-β cut-off algorithm. 4. Consider a room whose floor space is partitioned into equal sized blocks. Suppose there is a mobile robot (MR) in one block, and we want to move to a distant block. Some of the blocks are occupied with obstacles. The robot has to plan its trajectory so that it reaches the goal position from a given initial position without touching the obstacles. Can you design a heuristic function for the problem? If yes, solve the problem using the A* algorithm on a graph paper. Assume the location of the obstacles and the starting and the goal positions. References [1] Bender, E. A., Mathematical Methods in Artificial Intelligence, IEEE Computer Society Press, Los Alamitos, pp. 33-84, 1996. [2] Ginsberg, M., Essentials of Artificial Intelligence, Morgan Kaufmann, San Mateo, CA, pp. 49-103, 1993.
[3] Luger, G. F. and Stubblefield, W. A., Artificial Intelligence: Structures and Strategies for Complex Problem Solving, The Benjamin/ Cummings Publishing Co., Menlo Park, CA, pp.116-149, 1993. [4] Mahanti, A. and Daniels, J. C., “A SIMD approach to parallel heuristic search,” Artificial Intelligence, vol. 60, pp. 243-282, 1993. [5] Nilson, J. N., Principles of Artificial Intelligence, Morgan-Kaufmann, San Mateo, CA, pp. 112-126,1980. [6] Pearl, J., Heuristics: Intelligent Search Strategies for Computer Problem Solving, Addison-Wesley, Reading, MA, pp. 1-75, 1984. [7] Rich, E. and Knight, K., Artificial Intelligence, McGraw-Hill, New York, pp. 29-98, 1991. [8] Sarkar, S., Chakrabarti, P. P. and Ghose, S., “ A framework for learning in search-based systems,” IEEE Trans. on Knowledge and Data Engg., vol. 10, no. 4, July / Aug. 1998.
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Artificial Intelligence and Soft Co
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Library of Congress Cataloging-in-P
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understanding of the subject. The r
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4. Structural organization of the b
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ACKNOWLEDGMENT The author gratefull
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To my parents, Mr. Sailen Konar and
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Chapter 2: The Psychological Perspe
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5.4.2 Syntactic Methods for Theorem
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9.4.4 Realization of Fuzzy Inferenc
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Chapter 14: Machine Learning Using
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17.4.2.7 Fusing Multi-sensory Data
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22.4 Parallelism at Knowledge Repre
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1 Introduction to Artificial Intell
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instances of decision making [27],
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End. Begin state := new-states - ex
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(a) Generate and Test Approach: Thi
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this problem is useful for the foll
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disciplines. As a young discipline
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The bird and its attributes here ha
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[19] , Kosko [15] and Pedrycz [30]
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Reasoning in the presence of imprec
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where AI finds extensive applicatio
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M1 M2 M3 J2 J 1 8 5 J 2 J 1 2 8 J 2
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1.5.3 The Modern Period The modern
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A B AND C D E AND Y Fig. 1.12: A Pe
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improve reliability by realizing fr
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in AI problems, it supports massive
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[7] Dean, T., Allen, J. and Aloimon
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[34] Rajendra, C. and Chaudhury, D.
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2 The Psychological Perspective of
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The scope of realization of the pro
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2.2.3 Feature-based Approach for Pa
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From Sensory Registers Echoic Reg.
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cognitive memory and its utilizatio
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Tulving’s model bridges a potenti
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A " (a) (b) Fig. 2.6: The character
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his friend s facial image in memory
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sum need not be 180 degrees. Thus a
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same evening. Then he started medit
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construction of knowledge and its o
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saved in a magnetic media, which he
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set-point + error Controller Plant
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Cognitive science has emerged as a
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Further show that the Euclidean lea
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[4] Biswas, B., Mukherjee, A. K. an
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[28] Peterson, M. A., Kihlstrom, J.
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Production Systems, Logical Calculu
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against the data items of the WM. I
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Suppose the WM contains the data Bi
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To demonstrate the working principl
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i) Prefer rules for firing, where u
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In fig. 3.3, the antecedent clauses
Page 106 and 107: possible offspring states are gener
Page 108 and 109: Backward Reasoning: The backward re
Page 110 and 111: p q r s denotes joint premises t w
Page 112 and 113: 3.11.1 Isolation of Knowledge and C
Page 114 and 115: state, as the predecessor states of
Page 116 and 117: [3] Buchanan, B. G. and Shortliffe,
Page 118 and 119: issues: first ‘what to search’
Page 120 and 121: We will now present two typical alg
Page 122 and 123: Further, the first state within the
Page 124 and 125: n1 n2 n3 n8 (a) (b) (c) (d) (e) (f
Page 126 and 127: The iterative deepening search thus
Page 128 and 129: legal next states will also lie on
Page 130 and 131: End. Then push those children into
Page 132 and 133: Procedure Best-First-Search Begin 1
Page 134 and 135: End. have multiple parents; Under t
Page 136 and 137: node. Under this circumstance, the
Page 138 and 139: 6. Pn- Γ the set of paths from nod
Page 140 and 141: Therefore, f * (n’) = g* (n’) +
Page 142 and 143: 0 +10 B 1+3 C +4 D +5 E F G 2+2 3+1
Page 144 and 145: The above algorithm considers two d
Page 146 and 147: Step 1: X (7) Step 2: Step 3: U X (
Page 148 and 149: (iv) If all of the nodes connected
Page 150 and 151: If the values are propagated up to
Page 152 and 153: ii) the alpha value of any MAX node
Page 154 and 155: αmin =2 βmax =1 C αmin =1 e(n) =
Page 158 and 159: 5 The Logic of Propositions and Pre
Page 160 and 161: 5.2 Formal Definitions The followin
Page 162 and 163: Definition 5.7: A propositional for
Page 164 and 165: 5.4.1 Semantic Method for Theorem P
Page 166 and 167: 8. p \/ (q Λ ¬ q) ⇔ p 9. p Λ (
Page 168 and 169: ) AND, OR Removal: If the L.H.S. co
Page 170 and 171: Since all the terminals of the tree
Page 172 and 173: p v q ¬ q v r p v r ¬ p v s r v s
Page 174 and 175: Let AS = {A1, A2,, …..,An} be the
Page 176 and 177: 4. If P is a WFF and X is not a qua
Page 178 and 179: original expression: ( ¬ P11 ∨
Page 180 and 181: S: = S ∪ {variable or constant /
Page 182 and 183: ¬ Loves (john, mary) ¬Child (X)
Page 184 and 185: which implies that if q is true the
Page 186 and 187: ii) C is a ground instance of C [9]
Page 188 and 189: ) p→ (q→ r) ⇔ (p Λ q) → r
Page 190 and 191: [6] Leinweber, D., “Knowledge-bas
Page 192 and 193: of a ‘classroom scene’ interpre
Page 194 and 195: Sits-on (Y, bench, classhour), Pers
Page 196 and 197: Sits-on (mita, bench, classhour). 3
Page 198 and 199: Teacher (X) Sub-goal fails Person (
Page 200 and 201: Definition 6.5: A definite goal is
Page 202 and 203: Example 6.5, presented below, illus
Page 204 and 205: 6.6.1 Risk of Using CUT It is to be
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In the SLD tree for the Taxpayer pr
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6.9 Fixed Points in Non-Horn Clause
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6.11 Conclusions The main advantage
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preferred X50 >= 2, default X100
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7.1 Introduction Predicate Logic is
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proposed this logic and called it n
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We now present a few modal properti
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Expert Reasoning System New data Dy
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PR5: ¬Visits (Wife, market, Monday
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IN (n1) + IN (n2) + (n11) retracts
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may hold (and not must hold). An ex
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The resulting stable consequences t
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In this example, we call ψ = Bird
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important factor in non-monotonic r
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a) Boy(X) ∧ ¬ L ¬ Likes (X, cho
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8 Structured Approach to Knowledge
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predicate boy (jim). This can be re
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Consequently, we represent the abov
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Is-a Is-a Is-a Protozoa Bacteria Is
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Example 8.2: This example illustrat
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A common question that may be raise
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∴ q is true. 2) Defeasible deriva
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Examination Hall Seat Arrangement I
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Petri nets [5]. It, however, does n
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Since p1 and p 2 contain tokens and
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For building dependency structures,
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The most significant drawback of CD
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Once a script structure for a given
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[6] Nilsson, N. J., Principles of A
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techniques, we first introduce the
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of precision of data and certainty
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where D and S stand for disease and
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To illustrate the reasoning process
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2. It might happen that none of the
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One interesting property of Bayesia
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We now compute the messages that no
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The main steps [8], [12] of the bel
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Updating a node X thus involves upd
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j ↓ i→ round oval-shaped and MB
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Formally, the set of all possible o
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The orthogonal summation of belief
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The orthogonal summation operations
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integers, then we can definitely sa
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where a / b in fast-runner subset r
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where the “o” denotes a fuzzy A
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This may be formally written as µ
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cumulative maximum of the two succe
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“If you can manage to evaluate th
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[7] Shenoy, P. P. and Shafer, G.,
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10.1 Introduction Databases associa
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a finite set of places, D= {d1, d2
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µfast runner(x) 0.9 0.6 0.2 0.1 5
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present in the consequent part; Aug
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Procedure Cycle-detection (P, Q, m,
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Procedure Put-transition (Newlistk,
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The trace of the algorithm cycle- d
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p1 p2 pm n1 n2 nm Fig. 10.4: A tran
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where the elements qw / ∈ {0, 1}
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Q' m and Rm matrices. It may be not
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Definition 10.9: An arc is called p
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The procedure forward reasoning is
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In the above example, A, B, and C a
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n V (q k j ∧r j k ) to be close t
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Let us assume for the sake of simpl
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It is evident from the above distri
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= R b m o ((P ' f m) T o Nf c (t+1)
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Since such choice of Rfm and Rbm sa
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one step of belief revision in the
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10.9 Conclusions The chapter presen
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References [1] Bugarin, A. J. and B
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[24] Looney, C. G., "Fuzzy Petri ne
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11 Reasoning with Space and Time Th
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The other one is an extension by ne
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touches another, the common points
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Procedure Move-optimal (R , Startin
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at Jadavpur University verified thi
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µ above(θ) =sin 2 θ , when -∏
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c c a b q r a b (b) (a) d d p q r p
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11.5 Temporal Reasoning by Situatio
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Holds( now, rain-ceased) Axiom (3)
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Interpretation I Interpretation II
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Example 11.3: Prove that Ā(p) ≡
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11.6.3 Some Elementary Proofs in PT
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The second rule is generally called
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11.9 Conclusions The chapter demons
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12 Intelligent Planning This chapte
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sets opposite to the TV. So they oc
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where On (X, Y) means the object X
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this, let us consider the last prob
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(B), we generate the old state 3, w
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12.3 Least Commitment Planning The
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To start solving the problem, we fi
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We now have three partially ordered
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12.4 Hierarchical Task Network Plan
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d=0 d=1 d=2 d=3 Fig. 12.16: A hiera
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J1 J2 M1 M2 M3 or Job schedules J2
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job k from time 0. For example, the
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3. Design a hierarchical plan for t
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trainer, who supplies the input-out
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Definition 13.1: An object is an en
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The restriction of hypotheses can b
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Positive instances: 1. Object (larg
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To illustrate how LEX performs inte
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alive dead Z=A/W 2 1 0 0 1 2 Living
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where Pi denotes the proportion of
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3. Apply Mapping Function: Apply th
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determine the animals because it do
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simplest form of reinforcement lear
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Let us now assume that the game is
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How can we compute the utility valu
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13.5 Learning by Inductive Logic Pr
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know f ? These questions can be ans
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|H| (1-ε) m ≤ δ ⇒ m ≥ (1/ε
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[7] Michalski, R. S., “A theory a
Page 434 and 435:
However, most biologists are of the
Page 436 and 437:
The most common non-linear function
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(d) b1 a1 (e) c1 cj cq bi ah Fig.14
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transverse diameter, etc. as the in
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x 1 x 2 x n Penultimate layer ∑+F
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Drawbacks of back-propagation algor
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x1 x2 xn 14.6 Widrow-Hoff's Multi-l
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x 1 x 2 x 1 x 2 The training proces
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• If not, select another ADALINE,
Page 452 and 453:
ni 1 = '1' output ( firing ). Each
Page 454 and 455:
designed the weights (W) of a singl
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AND z1 s11 OR w11 w12 w 1n v 11 v12
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− ~ w X k, l ∼ = ⎡ ⎤ ⎢
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V x ∑ w O j = Sgn ( j+ ji i + A
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neural nets in the fields mentioned
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where the first summation is over a
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circuit,” IEEE Trans. on Circuits
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their joint usage in many problems,
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1 0 1 0 11 0 1 0 1 0 1 1 0 10 1 1 1
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15.2 Deterministic Explanation of H
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Thus, in a total of N selections wi
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and population size = 2, which mean
Page 478 and 479:
The behavior of GA without mutation
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a = ∑ Lt (π 0 P n ) i i=1 n→
Page 482 and 483:
Eθ GA Program Z1, Z2, Z3, Z4, X1,
Page 484 and 485:
e [W1 W2 W3 W4 W5 W6] T and [ G1 G2
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function. So, GA in each evolution
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f(x) = Sin (x) + [x * x + y] 1/2 ca
Page 490 and 491:
(EQ (DU(MT CS) (NOT CS)) (DU(MS NN)
Page 492 and 493:
[4] Chakraborty, U. K. and Muehlenb
Page 494 and 495:
16 Realizing Cognition Using Fuzzy
Page 496 and 497:
Cognitive maps are generally used f
Page 498 and 499:
Theorem 16.1: With initial values o
Page 500 and 501:
Here W T is a transposed weight mat
Page 502 and 503:
example, for moving one’s arm, th
Page 504 and 505:
and the weight adaptation equation
Page 506 and 507:
Xk+1 ∆Wk = α Ek οXk+1 T / ((Xk+
Page 508 and 509:
d5 d9 d1 d6 d7 d8 d10 d11 d1=Front
Page 510 and 511:
16.10 Conclusions and Future Direct
Page 512 and 513:
[6] Kosko, B., “Fuzzy cognitive m
Page 514 and 515:
however, have a narrow spectrum of
Page 516 and 517:
contaminated with it. However, for
Page 518 and 519:
1. Move the mask over the image, so
Page 520 and 521:
∇ 2 (g * f ) = ( ∇ 2 g ) * f. W
Page 522 and 523:
It may be noted that segmenting an
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machine has to narrate the game onl
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schematic diagram, briefly outlinin
Page 528 and 529:
same process for all clusters, we g
Page 530 and 531:
Level 1 Level 2 Level 0 Neuron Fig.
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I (u, v) YI Fig. 17.12: Camera mode
Page 534 and 535:
epipolar planes meet the image plan
Page 536 and 537:
(a, b, 1) Fig. 17.15: A 3-D represe
Page 538 and 539:
case III: Planes not parallel to th
Page 540 and 541:
yi = -fi (xi,* ai - 1*) + ( fi / a
Page 542 and 543:
Sample Execution: This is a program
Page 544 and 545:
U t11 t12 t13 t14 x V = t21 t22 t23
Page 546 and 547:
obtained after linearizing measurem
Page 548 and 549:
co-ordinate systems. The correspond
Page 550 and 551:
18 Linguistic Perception Building p
Page 552 and 553:
psychological aspects of understand
Page 554 and 555:
S NP VP ART N VP the man VP V NP ki
Page 556 and 557:
( S ( NP ( ( ART the ) (N man ) ) (
Page 558 and 559:
Sentence: NP VP 1 6 NP: ART N 2 ART
Page 560 and 561:
18.2.3.1 Learning For adaptation of
Page 562 and 563:
context sensitive grammar is thus m
Page 564 and 565:
Generally, we start the sentence S
Page 566 and 567:
VP: V NP S0 S1 Tagged procedure V:=
Page 568 and 569:
Laugh agent animal enjoyer entity p
Page 570 and 571:
18.5 Discourse and Pragmatic Analys
Page 572 and 573:
Thus the elements of communicative
Page 574 and 575:
19 Problem Solving by Constraint Sa
Page 576 and 577:
The recognition problem is the pres
Page 578 and 579:
CSP deals with two classical proble
Page 580 and 581:
= 10 10 = 10 = * Fig. 19.2 (b): Pro
Page 582 and 583:
+ _ V1 R1 V 2 V3 I1 I2 I3 V R2 R3 S
Page 584 and 585:
V = Now assuming the values of V, R
Page 586 and 587:
On (A, Ta) ∧ On (B, Ta) ∧On (C,
Page 588 and 589:
We now represent the neighboring re
Page 590 and 591:
Step 1: (x
Page 592 and 593:
such variable xj , xk, etc., attach
Page 594 and 595:
of C3. If the constraints are liste
Page 596 and 597:
The possible labels of the junction
Page 598 and 599:
The main part of CSP is the formula
Page 600 and 601:
20 Acquisition of Knowledge Acquisi
Page 602 and 603:
invite the experts to attend a meet
Page 604 and 605:
B E A= test ?, B = test results, C
Page 606 and 607:
The database in fig. 20.2 is extrac
Page 608 and 609:
20.5 Knowledge Refinement by Hebbia
Page 610 and 611:
* * * n i ( t + 1) = n i ( t ) at t
Page 612 and 613:
L(r,s) L(s,r) Y(r) Y(s) OS(r,s) n1
Page 614 and 615:
The FPN of fig. 20.5 is formed with
Page 616 and 617:
L(a,l) L(l,a) Y(a) Y(l) OS(a,l) n1
Page 618 and 619:
[3] Cooke, N. and Macdonald, J.,
Page 620 and 621:
21 Validation, Verification and Mai
Page 622 and 623:
Here the problem characteristic is
Page 624 and 625:
The chapter will cover various issu
Page 626 and 627:
21.2.1 Qualitative Methods for Perf
Page 628 and 629:
Paired t-test: Suppose xi ∈ X and
Page 630 and 631:
Ancestor P = {p1,p2} Tr = {tr1,tr2,
Page 632 and 633:
21.3.2 Inconsistencies in Knowledge
Page 634 and 635:
q tr1 tr2 p1 p2 …………… pn
Page 636 and 637:
A rule may also include a number of
Page 638 and 639:
21.4 Maintenance of Knowledge Based
Page 640 and 641:
control of data and knowledge is un
Page 642 and 643:
8. Stefik, M., Introduction to Know
Page 644 and 645:
are not suitable for AI application
Page 646 and 647:
Because of non-determinism in the s
Page 648 and 649:
Procedure Partial-Expansion Begin W
Page 650 and 651:
Step: Fig.22.4: A tree expanded by
Page 652 and 653:
Procedure Generous-Sharing Begin Fl
Page 654 and 655:
To evaluate the performance of the
Page 656 and 657:
Definition 22.2: If the antecedents
Page 658 and 659:
a) AND -Parallelism Consider a logi
Page 660 and 661:
However, given sufficient computing
Page 662 and 663:
EPN = { P, Tr, D, f, m, A, a, I, o
Page 664 and 665:
It is to be noted that if- then ope
Page 666 and 667:
After the bindings of the variables
Page 668 and 669:
F(x) ← A(X) , B(Y) (1) A(1) ← (
Page 670 and 671:
the result produced by clause (2) m
Page 672 and 673:
Else Flag:= true; End; Until no-of
Page 674 and 675:
transition for the PTVVM. The PTVVM
Page 676 and 677:
For the sake of convenience, the pi
Page 678 and 679:
22.6 Conclusions The chapter starte
Page 680 and 681:
Rule 3: S(X, Y) → Z (Y, X) Rule 4
Page 682 and 683:
23 Case Study I: Building a System
Page 684 and 685:
features in human faces and their r
Page 686 and 687:
Definition 23.4: A linear edge segm
Page 688 and 689:
lock containing edge. The productio
Page 690 and 691:
Definition 23.13: The measure of di
Page 692 and 693:
Partitioning Fe into Blocks Feature
Page 694 and 695:
The fuzzy membership functions used
Page 696 and 697:
∆ • Fig. 23.4: The delta and th
Page 698 and 699:
Thus we have altogether 6 different
Page 700 and 701:
cross-section of the vocal tract, w
Page 702 and 703:
23.4.2 Training a Multi-layered Neu
Page 704 and 705:
information with their normalized v
Page 706 and 707:
SR (Y, X) OR (M (X) ∧ M (Y) ∧ L
Page 708 and 709:
procedure, however, no attempts hav
Page 710 and 711:
23.5.5 Belief Revision and Limitcyc
Page 712 and 713:
that the inferences will be minimal
Page 714 and 715:
the formation of the FPN. The FPN o
Page 716 and 717:
is then initiated for detecting the
Page 718 and 719:
initial fuzzy beliefs at all places
Page 720 and 721:
at all feasible x, y. Then estimate
Page 722 and 723:
[13] Malmberg, B., Manual of Phonet
Page 724 and 725:
24.1 Mobile Robots Mobile robots ar
Page 726 and 727:
about its world. There exists ample
Page 728 and 729:
the process, else it attempts to fi
Page 730 and 731:
Depending on the type of planning p
Page 732 and 733:
WEST NORTH SOUTH Fig. 24.5: Represe
Page 734 and 735:
NW child B NE child 'C' SW child 'D
Page 736 and 737:
As observed from the node status, t
Page 738 and 739:
In their evolutionary planner algor
Page 740 and 741:
tuning of the path, such as avoidin
Page 742 and 743:
S S= starting point, G= Goal point,
Page 744 and 745:
Once the training is over, the syst
Page 746 and 747:
N o Table 24.2: Training pattern sa
Page 748 and 749:
24.9.1 Finite State Machine Finite
Page 750 and 751:
occurrence of a state, but also in
Page 752 and 753:
24.10 An Application in a Soccer Pl
Page 754 and 755:
Exercises 1. Devise an algorithm fo
Page 756 and 757:
[15] Meng, H. and Picton, P. D.,
Page 758 and 759:
24 + The Expectations from the Read
Page 760 and 761:
Appendix A How to Run the Sample Pr
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Predicate: LSR Argument1: S Argumen
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ANTECEDENT 1: Predicate: END conclu
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Rules properly arranged MAIN MENU:
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Level POSITION_FROM_LEFT NODE 1 1 H
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calculating membership values enter
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C > File currently in progress = ci
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When the goal is within concave obs
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path selected 160,160 and 240,240 T
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(a) Robot entering the room (b) Aft
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where tr and Outr denote the target
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∂E/∂Wsp = ∑r (∂E/∂Outr) (
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Proof of theorem10.2: For an oscill
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Thus, we get analogously , and 1 0
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= Q 'f m T o Rf m o ( Q ' f m o I )
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