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The recognition problem is the present content needs to check the geometric feature of the object under test and determine the object by satisfying the premises of one of the above three constraints. While dealing with CSP we should consider the following three issues: i) whether the constraints are satisfiable, i.e., does the problem has solutions that satisfy all the constraints? ii) simplification of the constraints by equivalent simpler ones, iii) optimization of the solution based on some other criteria, if more than one solution exists. 19.2 Formal Definitions We now present a few definitions, which will be referred to throughout the chapter. Definition 19.1: Constraints are mathematical/ logical relationships among the attributes of one or more objects. To understand the above definition, let us consider the ‘make-changes of 10$’ problem, where the 1$, 2$, 5$ notes are objects and their counts are the attributes in the problems. Thus the mathematical relationship among them is the expression ∑ ci xi = 10$ , which is the constraint. ∃xi Definition 19.2: The legitimate set of operators like ‘+’ , ‘* ’, ‘∧’ or ’∨’ and the type of the variables and their domains, the type of functions used and their range and the arguments of the operators are specified by a domain, called constraint domain. Formally, the constraint domain D is a 5 tuple, given by D={v, f, op, d, r} where v denotes the set of variables, f denotes the set of functions, op stands for the set of legal operators to be used on variables or functions, d is the domain of variable, and r is the range of the functions employed in the constraints.
Definition 19.3: A primitive constraint comprises of one or more constraint relation symbols together with their arguments, but cannot have a conjunction (Λ) in it. For example, x ≤2 , (x +y ) ≤ 2 are primitive constraints. Definition 19.4: A non-primitive or generic constraint is a conjunction (Λ) of primitive constraints. For example, (x+ y ≤ 2) Λ ( y ≤ 3 ) is a non-primitive constraint. Thus formally a constraint of the form C1 Λ C2 Λ ………….. Λ Cn, n>1 is a non-primitive constraint, when C1, C2, …………Cn all are primitive constraints [4]. Definition 19.5: A valuation θ for the set of variables v is an assignment of the values from the constraint domain to the variables v [4] . An expression E having variables v is given a value θ(E), computed by replacing the variable by its assigned value in the expression. For example, let v= {v1 ,v 2}; the domain of v1 , v2 being 1 ≤ v1 , v2 ≤2 ; let E= v1 2 + v2 2 ; now θ(E) = [v1 2 + v2 2 ] v1 =x , v2 = y where 1 ≤ x, y ≤ 2. Definition 19.6: A constraint is called satisfiable, if there exists at least one solution satisfying the constraint. For instance, {(x+ y ≤2 ) ∧ ( 0 ≤x, y ≤2 ) } are satisfiable constraints for integer x, y as there exists a solution x = y =1 that satisfies the constraints. On the other hand, {(x+ y ≤ 2) ∧ ( x >2) ∧ (y>2)} does not have a solution for integer x, y. Consequently, constraint (x+ y ≤ 2) ∧ ( x > 2) ∧ (y > 2 ) is called unsatisfiable. Definition 19.7: Two constraints C1 and C2 having same solution set are called equivalent and the equivalent relation between C1 and C2 is denoted by C1 ↔ C2 . For example, C1 = { (x+ y ≤ 2) Λ (x=1) Λ (y0)} and C2= { (x+ y ≤ 2) Λ (0< x) Λ (x≤2) Λ (0
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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
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possible offspring states are gener
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Backward Reasoning: The backward re
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p q r s denotes joint premises t w
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3.11.1 Isolation of Knowledge and C
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state, as the predecessor states of
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[3] Buchanan, B. G. and Shortliffe,
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issues: first ‘what to search’
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We will now present two typical alg
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Further, the first state within the
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n1 n2 n3 n8 (a) (b) (c) (d) (e) (f
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The iterative deepening search thus
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legal next states will also lie on
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End. Then push those children into
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Procedure Best-First-Search Begin 1
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End. have multiple parents; Under t
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node. Under this circumstance, the
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6. Pn- Γ the set of paths from nod
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Therefore, f * (n’) = g* (n’) +
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0 +10 B 1+3 C +4 D +5 E F G 2+2 3+1
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The above algorithm considers two d
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Step 1: X (7) Step 2: Step 3: U X (
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(iv) If all of the nodes connected
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If the values are propagated up to
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ii) the alpha value of any MAX node
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αmin =2 βmax =1 C αmin =1 e(n) =
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eductions. Constraint satisfaction
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5 The Logic of Propositions and Pre
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5.2 Formal Definitions The followin
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Definition 5.7: A propositional for
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5.4.1 Semantic Method for Theorem P
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8. p \/ (q Λ ¬ q) ⇔ p 9. p Λ (
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) AND, OR Removal: If the L.H.S. co
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Since all the terminals of the tree
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p v q ¬ q v r p v r ¬ p v s r v s
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Let AS = {A1, A2,, …..,An} be the
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4. If P is a WFF and X is not a qua
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original expression: ( ¬ P11 ∨
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S: = S ∪ {variable or constant /
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¬ Loves (john, mary) ¬Child (X)
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which implies that if q is true the
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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
Page 526 and 527: 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.
Page 532 and 533: 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 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
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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
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
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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
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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
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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
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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
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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
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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
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
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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
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about its world. There exists ample
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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
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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
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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.,
Page 758 and 759:
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
Page 788:
= Q 'f m T o Rf m o ( Q ' f m o I )
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