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6. Pn- Γ the set of paths from node n to the set of goals Γ 7. g* (n) the cheapest cost of paths, going from starting (root) node s to node n, g* (n) = K (s, n) 8. h* (n) the cheapest cost of paths, going from node n to Γ, h* (n) = Min K (n, γ) , for all γ ε Γ 9. C* the cheapest cost of paths going from s to Γ, C* = h* (s) We now define the following properties of best first search algorithms. a) Completeness: An algorithm is said to be complete, if it terminates with a solution, when one exists. b) Admissibility: An algorithm is called admissible if it is guaranteed to return an optimal solution, whenever a solution exists. c) Dominance: An algorithm A1 is said to dominate A2, if every node expanded by A1 is also expanded by A2. d) Optimality: An algorithm is said to be optimal over a class of algorithms, if it dominates all members of the class. We now present here some of the interesting properties of the heuristic functions. Property I: Any node n* on an optimal path P* γ - Γ always satisfies equation (4.1) f*(n*)=C* (4.1) where C* is the cheapest cost from s to Γ.
Proof: f * (n* ) = g* (n* ) + h* (n* ) = K (s, n*) + Min K (n*, γ) γ ε Γ = Min K (s, γ ) γ ε Γ = C* . The following results directly follow from property I. i) f* (s) = C* and ii) f* (γ) = C* . Property II: Any node n that does not lie on any of the optimal paths P*s-Γ satisfies inequality (4.2). f * (n) > C*. (4.2) Proof: Proof is straightforward and is therefore omitted. Definition 4.3: An heuristic function h is said to be admissible [6] if h (n) ≤ h* (n) . Property III: At any time before A* terminates, there exists an open node n’ on P* s- -Γ with f (n’) ≤ C* . Proof: Consider an optimal path P* s- -γ belonging to P* s- -Γ . Let P* s- -γ = s, n1, n2...,n’,...,γ and let n’ be the shallowest (minimum depth) open node on P’ s- -Γ . Since γ is not closed before termination, n’ is an open node. Further, since all ancestors of n’ are closed and since the path s,n1,n2,..., n’ is optimal, therefore, it must be that the pointers of n’ are along P*s-n’ . Therefore, g (n’) = g* (n’).
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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
Page 88 and 89: Further show that the Euclidean lea
Page 90 and 91: [4] Biswas, B., Mukherjee, A. K. an
Page 92 and 93: [28] Peterson, M. A., Kihlstrom, J.
Page 94 and 95: Production Systems, Logical Calculu
Page 96 and 97: against the data items of the WM. I
Page 98 and 99: Suppose the WM contains the data Bi
Page 100 and 101: To demonstrate the working principl
Page 102 and 103: i) Prefer rules for firing, where u
Page 104 and 105: 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 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 156 and 157: eductions. Constraint satisfaction
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]
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) p→ (q→ r) ⇔ (p Λ q) → r
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[6] Leinweber, D., “Knowledge-bas
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of a ‘classroom scene’ interpre
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Sits-on (Y, bench, classhour), Pers
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Sits-on (mita, bench, classhour). 3
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Teacher (X) Sub-goal fails Person (
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Definition 6.5: A definite goal is
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Example 6.5, presented below, illus
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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
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However, most biologists are of the
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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,
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ni 1 = '1' output ( firing ). Each
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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
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The behavior of GA without mutation
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a = ∑ Lt (π 0 P n ) i i=1 n→
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Eθ GA Program Z1, Z2, Z3, Z4, X1,
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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
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(EQ (DU(MT CS) (NOT CS)) (DU(MS NN)
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[4] Chakraborty, U. K. and Muehlenb
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16 Realizing Cognition Using Fuzzy
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Cognitive maps are generally used f
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Theorem 16.1: With initial values o
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Here W T is a transposed weight mat
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example, for moving one’s arm, th
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and the weight adaptation equation
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Xk+1 ∆Wk = α Ek οXk+1 T / ((Xk+
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d5 d9 d1 d6 d7 d8 d10 d11 d1=Front
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16.10 Conclusions and Future Direct
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[6] Kosko, B., “Fuzzy cognitive m
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however, have a narrow spectrum of
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contaminated with it. However, for
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1. Move the mask over the image, so
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∇ 2 (g * f ) = ( ∇ 2 g ) * f. W
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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
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same process for all clusters, we g
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Level 1 Level 2 Level 0 Neuron Fig.
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I (u, v) YI Fig. 17.12: Camera mode
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epipolar planes meet the image plan
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(a, b, 1) Fig. 17.15: A 3-D represe
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case III: Planes not parallel to th
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yi = -fi (xi,* ai - 1*) + ( fi / a
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Sample Execution: This is a program
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U t11 t12 t13 t14 x V = t21 t22 t23
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obtained after linearizing measurem
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co-ordinate systems. The correspond
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18 Linguistic Perception Building p
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psychological aspects of understand
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S NP VP ART N VP the man VP V NP ki
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( S ( NP ( ( ART the ) (N man ) ) (
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Sentence: NP VP 1 6 NP: ART N 2 ART
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18.2.3.1 Learning For adaptation of
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context sensitive grammar is thus m
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Generally, we start the sentence S
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VP: V NP S0 S1 Tagged procedure V:=
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Laugh agent animal enjoyer entity p
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18.5 Discourse and Pragmatic Analys
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Thus the elements of communicative
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19 Problem Solving by Constraint Sa
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The recognition problem is the pres
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CSP deals with two classical proble
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= 10 10 = 10 = * Fig. 19.2 (b): Pro
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+ _ V1 R1 V 2 V3 I1 I2 I3 V R2 R3 S
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V = Now assuming the values of V, R
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On (A, Ta) ∧ On (B, Ta) ∧On (C,
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We now represent the neighboring re
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Step 1: (x
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such variable xj , xk, etc., attach
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of C3. If the constraints are liste
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The possible labels of the junction
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The main part of CSP is the formula
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20 Acquisition of Knowledge Acquisi
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invite the experts to attend a meet
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B E A= test ?, B = test results, C
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The database in fig. 20.2 is extrac
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20.5 Knowledge Refinement by Hebbia
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* * * n i ( t + 1) = n i ( t ) at t
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L(r,s) L(s,r) Y(r) Y(s) OS(r,s) n1
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The FPN of fig. 20.5 is formed with
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L(a,l) L(l,a) Y(a) Y(l) OS(a,l) n1
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[3] Cooke, N. and Macdonald, J.,
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21 Validation, Verification and Mai
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Here the problem characteristic is
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The chapter will cover various issu
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21.2.1 Qualitative Methods for Perf
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Paired t-test: Suppose xi ∈ X and
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Ancestor P = {p1,p2} Tr = {tr1,tr2,
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21.3.2 Inconsistencies in Knowledge
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q tr1 tr2 p1 p2 …………… pn
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A rule may also include a number of
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21.4 Maintenance of Knowledge Based
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control of data and knowledge is un
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8. Stefik, M., Introduction to Know
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are not suitable for AI application
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Because of non-determinism in the s
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Procedure Partial-Expansion Begin W
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Step: Fig.22.4: A tree expanded by
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Procedure Generous-Sharing Begin Fl
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To evaluate the performance of the
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Definition 22.2: If the antecedents
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a) AND -Parallelism Consider a logi
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However, given sufficient computing
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EPN = { P, Tr, D, f, m, A, a, I, o
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It is to be noted that if- then ope
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After the bindings of the variables
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F(x) ← A(X) , B(Y) (1) A(1) ← (
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the result produced by clause (2) m
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Else Flag:= true; End; Until no-of
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transition for the PTVVM. The PTVVM
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For the sake of convenience, the pi
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22.6 Conclusions The chapter starte
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Rule 3: S(X, Y) → Z (Y, X) Rule 4
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23 Case Study I: Building a System
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features in human faces and their r
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Definition 23.4: A linear edge segm
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lock containing edge. The productio
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Definition 23.13: The measure of di
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Partitioning Fe into Blocks Feature
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The fuzzy membership functions used
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∆ • Fig. 23.4: The delta and th
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Thus we have altogether 6 different
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cross-section of the vocal tract, w
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23.4.2 Training a Multi-layered Neu
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information with their normalized v
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SR (Y, X) OR (M (X) ∧ M (Y) ∧ L
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procedure, however, no attempts hav
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23.5.5 Belief Revision and Limitcyc
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that the inferences will be minimal
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the formation of the FPN. The FPN o
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is then initiated for detecting the
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initial fuzzy beliefs at all places
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at all feasible x, y. Then estimate
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[13] Malmberg, B., Manual of Phonet
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24.1 Mobile Robots Mobile robots ar
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about its world. There exists ample
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the process, else it attempts to fi
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Depending on the type of planning p
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WEST NORTH SOUTH Fig. 24.5: Represe
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NW child B NE child 'C' SW child 'D
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As observed from the node status, t
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In their evolutionary planner algor
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tuning of the path, such as avoidin
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S S= starting point, G= Goal point,
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Once the training is over, the syst
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N o Table 24.2: Training pattern sa
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24.9.1 Finite State Machine Finite
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occurrence of a state, but also in
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24.10 An Application in a Soccer Pl
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Exercises 1. Devise an algorithm fo
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[15] Meng, H. and Picton, P. D.,
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24 + The Expectations from the Read
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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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Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

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