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Petri nets [5]. It, however, does not mean that Petri nets can be used as an automated tool for FOL based reasoning only. In fact, Petri nets can be used for reasoning with a rule based system or (and) can be extended to handle uncertainties modeled with stochastic and fuzzy techniques. A separate chapter on fuzzy Petri nets thus has been covered in the book, keeping in mind its increasing demand in knowledge engineering. Let us now represent the following FOL clauses by a Petri net. FOL clauses Rule1: Father (X,Y) Son (Y,X) ∨ Daughter (Y,X). Rule2: Daughter (Y,X) ∧ Female (X) Mother (X,Y). The Petri net of 8.13 describes the above rules. It is to be noted that the variables are recorded against the arc. The argument of the valid predicate recorded against the arc is called an arc function. The input arc functions of a transition are positive, while the output arc functions are negative. Reasoning: For reasoning, one has to assign the atomic clauses in the Petri net. For instance let us assume that we are given the following clauses: Rule3: Father (d, r) Rule4: ¬Son (r, d) Rule5: ¬Mother (k, l) Rule6: Female (k) The arguent of the above clauses along with the sign of the predicates is assigned as tokens (inside places) in the Petri net (vide fig. 8.14). The following rules of transition firing are then used to derive the resulting instances. 1. A transition is enabled in the forward direction, if all its input places and all but one of its output places possess properly signed tokens with ‘consistent variable bindings’. Consistent variable bindings are checked by the following procedure: i) The value of signed variables in the arc function is bound with the signed tokens of the associated places. ii) The above process is repeated for all the arc functions associated with the transition.
iii) The common value of each (sign-free) variable is then identified. The value of the set of variables, thus obtained, for each transition is called consistent bindings. 2. A transition is enabled in the backward direction, if all its output places and all but one of its input places possess consistent bindings. Father P1 (X, Y) tr1 An arc function ¬(Y,X) ¬(Y, X) Son Daughter Female (Y,X) ¬(X,Y) An arc function at the output (input) arc of a transition is negative (positive). Fig. 8.13: A Petri net representing FOL clauses. An enabled transition fires by generating tokens following the arc function but with opposite sign of the arc functions and saves it at appropriate places, associated with the transition. However, a multiple copy of the same token is not kept at a given place. With reference to fig. 8.14, we find for transition tr1 two set of bindings X = d , Y = r (see place p1 and the associated arc function) and ¬Y = ¬ r , ¬X = ¬ d (see place p 2 and the associated arc function). The resulting consistent binding for tr1 is thus X = d & Y= r . P2 P3 P5 (X) A place A transition tr2 Mother P4
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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
Page 202 and 203: Example 6.5, presented below, illus
Page 204 and 205: 6.6.1 Risk of Using CUT It is to be
Page 206 and 207: In the SLD tree for the Taxpayer pr
Page 208 and 209: 6.9 Fixed Points in Non-Horn Clause
Page 210 and 211: 6.11 Conclusions The main advantage
Page 212 and 213: preferred X50 >= 2, default X100
Page 214 and 215: 7.1 Introduction Predicate Logic is
Page 216 and 217: proposed this logic and called it n
Page 218 and 219: We now present a few modal properti
Page 220 and 221: Expert Reasoning System New data Dy
Page 222 and 223: PR5: ¬Visits (Wife, market, Monday
Page 224 and 225: IN (n1) + IN (n2) + (n11) retracts
Page 226 and 227: may hold (and not must hold). An ex
Page 228 and 229: The resulting stable consequences t
Page 230 and 231: In this example, we call ψ = Bird
Page 232 and 233: important factor in non-monotonic r
Page 234 and 235: a) Boy(X) ∧ ¬ L ¬ Likes (X, cho
Page 236 and 237: 8 Structured Approach to Knowledge
Page 238 and 239: predicate boy (jim). This can be re
Page 240 and 241: Consequently, we represent the abov
Page 242 and 243: Is-a Is-a Is-a Protozoa Bacteria Is
Page 244 and 245: Example 8.2: This example illustrat
Page 246 and 247: A common question that may be raise
Page 248 and 249: ∴ q is true. 2) Defeasible deriva
Page 250 and 251: Examination Hall Seat Arrangement I
Page 254 and 255: Since p1 and p 2 contain tokens and
Page 256 and 257: For building dependency structures,
Page 258 and 259: The most significant drawback of CD
Page 260 and 261: Once a script structure for a given
Page 262 and 263: [6] Nilsson, N. J., Principles of A
Page 264 and 265: techniques, we first introduce the
Page 266 and 267: of precision of data and certainty
Page 268 and 269: where D and S stand for disease and
Page 270 and 271: To illustrate the reasoning process
Page 272 and 273: 2. It might happen that none of the
Page 274 and 275: One interesting property of Bayesia
Page 276 and 277: We now compute the messages that no
Page 278 and 279: The main steps [8], [12] of the bel
Page 280 and 281: Updating a node X thus involves upd
Page 282 and 283: j ↓ i→ round oval-shaped and MB
Page 284 and 285: Formally, the set of all possible o
Page 286 and 287: The orthogonal summation of belief
Page 288 and 289: The orthogonal summation operations
Page 290 and 291: integers, then we can definitely sa
Page 292 and 293: where a / b in fast-runner subset r
Page 294 and 295: where the “o” denotes a fuzzy A
Page 296 and 297: This may be formally written as µ
Page 298 and 299: cumulative maximum of the two succe
Page 300 and 301: “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
Page 478 and 479:
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,
Page 484 and 485:
e [W1 W2 W3 W4 W5 W6] T and [ G1 G2
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function. So, GA in each evolution
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f(x) = Sin (x) + [x * x + y] 1/2 ca
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(EQ (DU(MT CS) (NOT CS)) (DU(MS NN)
Page 492 and 493:
[4] Chakraborty, U. K. and Muehlenb
Page 494 and 495:
16 Realizing Cognition Using Fuzzy
Page 496 and 497:
Cognitive maps are generally used f
Page 498 and 499:
Theorem 16.1: With initial values o
Page 500 and 501:
Here W T is a transposed weight mat
Page 502 and 503:
example, for moving one’s arm, th
Page 504 and 505:
and the weight adaptation equation
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Xk+1 ∆Wk = α Ek οXk+1 T / ((Xk+
Page 508 and 509:
d5 d9 d1 d6 d7 d8 d10 d11 d1=Front
Page 510 and 511:
16.10 Conclusions and Future Direct
Page 512 and 513:
[6] Kosko, B., “Fuzzy cognitive m
Page 514 and 515:
however, have a narrow spectrum of
Page 516 and 517:
contaminated with it. However, for
Page 518 and 519:
1. Move the mask over the image, so
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∇ 2 (g * f ) = ( ∇ 2 g ) * f. W
Page 522 and 523:
It may be noted that segmenting an
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machine has to narrate the game onl
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schematic diagram, briefly outlinin
Page 528 and 529:
same process for all clusters, we g
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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
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
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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
Page 550 and 551:
18 Linguistic Perception Building p
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psychological aspects of understand
Page 554 and 555:
S NP VP ART N VP the man VP V NP ki
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( 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
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context sensitive grammar is thus m
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Generally, we start the sentence S
Page 566 and 567:
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
Page 578 and 579:
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
Page 584 and 585:
V = Now assuming the values of V, R
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On (A, Ta) ∧ On (B, Ta) ∧On (C,
Page 588 and 589:
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
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
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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
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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
Page 614 and 615:
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
Page 618 and 619:
[3] Cooke, N. and Macdonald, J.,
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21 Validation, Verification and Mai
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Here the problem characteristic is
Page 624 and 625:
The chapter will cover various issu
Page 626 and 627:
21.2.1 Qualitative Methods for Perf
Page 628 and 629:
Paired t-test: Suppose xi ∈ X and
Page 630 and 631:
Ancestor P = {p1,p2} Tr = {tr1,tr2,
Page 632 and 633:
21.3.2 Inconsistencies in Knowledge
Page 634 and 635:
q tr1 tr2 p1 p2 …………… pn
Page 636 and 637:
A rule may also include a number of
Page 638 and 639:
21.4 Maintenance of Knowledge Based
Page 640 and 641:
control of data and knowledge is un
Page 642 and 643:
8. Stefik, M., Introduction to Know
Page 644 and 645:
are not suitable for AI application
Page 646 and 647:
Because of non-determinism in the s
Page 648 and 649:
Procedure Partial-Expansion Begin W
Page 650 and 651:
Step: Fig.22.4: A tree expanded by
Page 652 and 653:
Procedure Generous-Sharing Begin Fl
Page 654 and 655:
To evaluate the performance of the
Page 656 and 657:
Definition 22.2: If the antecedents
Page 658 and 659:
a) AND -Parallelism Consider a logi
Page 660 and 661:
However, given sufficient computing
Page 662 and 663:
EPN = { P, Tr, D, f, m, A, a, I, o
Page 664 and 665:
It is to be noted that if- then ope
Page 666 and 667:
After the bindings of the variables
Page 668 and 669:
F(x) ← A(X) , B(Y) (1) A(1) ← (
Page 670 and 671:
the result produced by clause (2) m
Page 672 and 673:
Else Flag:= true; End; Until no-of
Page 674 and 675:
transition for the PTVVM. The PTVVM
Page 676 and 677:
For the sake of convenience, the pi
Page 678 and 679:
22.6 Conclusions The chapter starte
Page 680 and 681:
Rule 3: S(X, Y) → Z (Y, X) Rule 4
Page 682 and 683:
23 Case Study I: Building a System
Page 684 and 685:
features in human faces and their r
Page 686 and 687:
Definition 23.4: A linear edge segm
Page 688 and 689:
lock containing edge. The productio
Page 690 and 691:
Definition 23.13: The measure of di
Page 692 and 693:
Partitioning Fe into Blocks Feature
Page 694 and 695:
The fuzzy membership functions used
Page 696 and 697:
∆ • Fig. 23.4: The delta and th
Page 698 and 699:
Thus we have altogether 6 different
Page 700 and 701:
cross-section of the vocal tract, w
Page 702 and 703:
23.4.2 Training a Multi-layered Neu
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information with their normalized v
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SR (Y, X) OR (M (X) ∧ M (Y) ∧ L
Page 708 and 709:
procedure, however, no attempts hav
Page 710 and 711:
23.5.5 Belief Revision and Limitcyc
Page 712 and 713:
that the inferences will be minimal
Page 714 and 715:
the formation of the FPN. The FPN o
Page 716 and 717:
is then initiated for detecting the
Page 718 and 719:
initial fuzzy beliefs at all places
Page 720 and 721:
at all feasible x, y. Then estimate
Page 722 and 723:
[13] Malmberg, B., Manual of Phonet
Page 724 and 725:
24.1 Mobile Robots Mobile robots ar
Page 726 and 727:
about its world. There exists ample
Page 728 and 729:
the process, else it attempts to fi
Page 730 and 731:
Depending on the type of planning p
Page 732 and 733:
WEST NORTH SOUTH Fig. 24.5: Represe
Page 734 and 735:
NW child B NE child 'C' SW child 'D
Page 736 and 737:
As observed from the node status, t
Page 738 and 739:
In their evolutionary planner algor
Page 740 and 741:
tuning of the path, such as avoidin
Page 742 and 743:
S S= starting point, G= Goal point,
Page 744 and 745:
Once the training is over, the syst
Page 746 and 747:
N o Table 24.2: Training pattern sa
Page 748 and 749:
24.9.1 Finite State Machine Finite
Page 750 and 751:
occurrence of a state, but also in
Page 752 and 753:
24.10 An Application in a Soccer Pl
Page 754 and 755:
Exercises 1. Devise an algorithm fo
Page 756 and 757:
[15] Meng, H. and Picton, P. D.,
Page 758 and 759:
24 + The Expectations from the Read
Page 760 and 761:
Appendix A How to Run the Sample Pr
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Predicate: LSR Argument1: S Argumen
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ANTECEDENT 1: Predicate: END conclu
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Rules properly arranged MAIN MENU:
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Level POSITION_FROM_LEFT NODE 1 1 H
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calculating membership values enter
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C > File currently in progress = ci
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When the goal is within concave obs
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path selected 160,160 and 240,240 T
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(a) Robot entering the room (b) Aft
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where tr and Outr denote the target
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∂E/∂Wsp = ∑r (∂E/∂Outr) (
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Proof of theorem10.2: For an oscill
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Thus, we get analogously , and 1 0
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= Q 'f m T o Rf m o ( Q ' f m o I )
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Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

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