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EPN = { P, Tr, D, f, m, A, a, I, o } where P = {p1, p2,……, pm} is a set of places, Tr = {tr1, tr2,……, trm} is a set of transitions, D = {d1, d2,……, dm} is a set of predicates, P ∩ Tr ∩ D = φ, Cardinality of P = Cardinality of D, f: D → P ∝ represents a mapping from the set of predicates to the set of places, m: P→ (xi, …, yi , X, …….,Y ) is an association function, represented by the mapping from places to terms, which may include both constant(s), variable(s) and function of variables, A: (P→ Tr ) ∪ (Tr→ P) is the set of arcs, representing the mapping from the places to the transitions and vice versa, a: A→ (X, Y,…., Z) is an association function of the arcs, represented by the mapping from the arcs to terms, I: Tr→ P is a set of input places, represented by the mapping from the transitions to their input places, 0: Tr → P is a set of output places, represented by the mapping from the transitions to their output places. Example 22.2: A Petri net consists of places, transitions, tokens at places and are functions. A detailed representation of the given rules with Petri nets is presented in fig. 22.10. Given rules: Son (Y, Z), Daughter (Y, Z) ← Father (X, Y), Wife (Z, X) . Father (r, l) ← Wife (s, r) ← ¬ Daughter (l, s) ←
It may be noted that the first rule includes two literals in the head, while the last rule includes negated literal in the head, both of which are violated in standard logic programs, but valid in predicate logic. p1 Father p2 Wife A1 A2 (X, Y) ¬(Y, Z) (Z, X) ¬ (Y, Z) Fig. 22.10: Parameters of an EPN used to represent knowledge in predicate logic. Here, P = {p1 , p2 , p3 , p4 }, Tr = {tr1}, D = {Father, Wife, Son , Daughter }, f(Father ) = p1 , f (Wife) = p2 , f(Son) = p3 , f (Daughter) = p4 , tr1 m(p1) = , m(p2 ) = , m(p3 ) = < φ > , m(p4 ) = ¬ initially and can be computed subsequently through unification of predicates in the process of resolution of clauses. A = {A1, A2, A3 , A4}, a (A1) = (X, Y) , a (A2 ) = (Z, X) , a (A3 ) = ¬ (Y, Z) , a (A4 ) = ¬ (Y, Z) are the arc functions, I(tr1 ) = {p1 , p2 }, and 0(tr2 ) = {p3 ,p4 }. A3 A4 p3 Son ¬ p4 Daughter
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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
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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
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 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
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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
Page 752 and 753:
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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