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The second rule is generally called weak negation, which is in contrast to the following rule, called strong negation. ∀t , ( t1 ≤t) ∧ (t2 ≥ t) ∧ Holds(t1, t2, ¬ φ) ¬ Holds(t, φ) . The weak and strong negation both support the following properties: For weak negation, ├ Holds(t1, t2, ¬ ¬ q) ├ ¬Holds(t1, t2, ¬ q) ├ ¬¬Holds(t1, t2, q) ├ Holds (t1, t2, q). For strong negation, ├ ∀ t , ( t1 ≤ t) ∧ (t2 ≥ t) ∧ Holds(t1, t2, ¬ ¬p) ├ ∀ t , ( t1 ≤ t) ∧ (t2 ≥ t) ∧ ¬ Holds(t1, t2, ¬p) ├ ∀ t , ( t1 ≤t) ∧ (t2 ≥ t) ∧ ¬ ¬ Holds(t1, t2, p) ├ ∀t , ( t1 ≤t) ∧ (t2 ≥ t) ∧ Holds(t1, t2, p). But there exists evidence of proving Holds(t1, t2, p) ∨ Holds(t1, t2, q) from Holds(t1, t2, p∨q), which is not feasible by strong negation [3]. 11.8 Reasoning with Both Space and Time We have discussed various schemes for reasoning with space and time independently. However, there exist circumstances, when both are required concurrently. A formalization of reasoning techniques in variation of both spatial and temporal events is an open area of research till date. We here just illustrate the justification of such reasoning with an example. Example 11.8: Suppose one summer evening, a hot burst of wind moving in the west causes a fire at the hill, which gradually started spreading in the village (Fig. 11.10). A villager reports to the fire brigade station at time t1. A fire brigade now has to plan the route, so that it can reach the village at the earliest. There are only two roads, one the hillside road (road1) that requires longer time of traversal and the other road (road2) which requires crossing a river through a bridge to reach the village. The pilot of the fire brigade car thinks that it can reach E1 end of the bridge within 15 minutes, but crossing the river after 15 minutes will be difficult, as by that time many villagers too will rush to cross it from other end E2 of the bridge. But traversal through the road1 will require 20 minutes more than the time required through road2 had
there been no rush. So, the main question that remains: will the villagers, who reached the end E2 of the bridge within 15 minutes of the breaking out of fire in the village, vacate the village within 35 minutes? The decision of the pilot in selecting the right road depends solely on this answer. To resolve this, the fire brigade station-master observed the scenario in the village by moving up a high tower and found a few villagers rushing towards E2 and instructed his men to go to the spot through road2. forest village E2 Hill wind flow river road1 E1 bridge road2 Fire brigade station Fig. 11.10: The topological map of a hillside village and its surroundings. The above story requires a spatial representation of the map and then reasoning about time. Here the spatial changes of the villagers and the fire brigade must be taken into account at specific time slots. Readers may try to formulate the (temporal part of the) problem by situation calculus and define the spatial part as FOL clauses. So, spatial changes can be reflected in different time frames. The non-monotonism in the problem can also be resolved by the qualification method presented under situation calculus.
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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}
Page 322 and 323: Q' m and Rm matrices. It may be not
Page 324 and 325: Definition 10.9: An arc is called p
Page 326 and 327: The procedure forward reasoning is
Page 328 and 329: In the above example, A, B, and C a
Page 330 and 331: n V (q k j ∧r j k ) to be close t
Page 332 and 333: Let us assume for the sake of simpl
Page 334 and 335: It is evident from the above distri
Page 336 and 337: = R b m o ((P ' f m) T o Nf c (t+1)
Page 338 and 339: Since such choice of Rfm and Rbm sa
Page 340 and 341: one step of belief revision in the
Page 342 and 343: 10.9 Conclusions The chapter presen
Page 344 and 345: References [1] Bugarin, A. J. and B
Page 346 and 347: [24] Looney, C. G., "Fuzzy Petri ne
Page 348 and 349: 11 Reasoning with Space and Time Th
Page 350 and 351: The other one is an extension by ne
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Page 354 and 355: Procedure Move-optimal (R , Startin
Page 356 and 357: at Jadavpur University verified thi
Page 358 and 359: µ above(θ) =sin 2 θ , when -∏
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Page 362 and 363: 11.5 Temporal Reasoning by Situatio
Page 364 and 365: Holds( now, rain-ceased) Axiom (3)
Page 366 and 367: Interpretation I Interpretation II
Page 368 and 369: Example 11.3: Prove that Ā(p) ≡
Page 370 and 371: 11.6.3 Some Elementary Proofs in PT
Page 374 and 375: 11.9 Conclusions The chapter demons
Page 376 and 377: 12 Intelligent Planning This chapte
Page 378 and 379: sets opposite to the TV. So they oc
Page 380 and 381: where On (X, Y) means the object X
Page 382 and 383: this, let us consider the last prob
Page 384 and 385: (B), we generate the old state 3, w
Page 386 and 387: 12.3 Least Commitment Planning The
Page 388 and 389: To start solving the problem, we fi
Page 390 and 391: We now have three partially ordered
Page 392 and 393: 12.4 Hierarchical Task Network Plan
Page 394 and 395: d=0 d=1 d=2 d=3 Fig. 12.16: A hiera
Page 396 and 397: J1 J2 M1 M2 M3 or Job schedules J2
Page 398 and 399: job k from time 0. For example, the
Page 400 and 401: 3. Design a hierarchical plan for t
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Page 404 and 405: Definition 13.1: An object is an en
Page 406 and 407: The restriction of hypotheses can b
Page 408 and 409: Positive instances: 1. Object (larg
Page 410 and 411: To illustrate how LEX performs inte
Page 412 and 413: alive dead Z=A/W 2 1 0 0 1 2 Living
Page 414 and 415: where Pi denotes the proportion of
Page 416 and 417: 3. Apply Mapping Function: Apply th
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Page 420 and 421: simplest form of reinforcement lear
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Let us now assume that the game is
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How can we compute the utility valu
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13.5 Learning by Inductive Logic Pr
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know f ? These questions can be ans
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|H| (1-ε) m ≤ δ ⇒ m ≥ (1/ε
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[7] Michalski, R. S., “A theory a
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However, most biologists are of the
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The most common non-linear function
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(d) b1 a1 (e) c1 cj cq bi ah Fig.14
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transverse diameter, etc. as the in
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x 1 x 2 x n Penultimate layer ∑+F
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Drawbacks of back-propagation algor
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x1 x2 xn 14.6 Widrow-Hoff's Multi-l
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x 1 x 2 x 1 x 2 The training proces
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• If not, select another ADALINE,
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ni 1 = '1' output ( firing ). Each
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designed the weights (W) of a singl
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AND z1 s11 OR w11 w12 w 1n v 11 v12
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− ~ w X k, l ∼ = ⎡ ⎤ ⎢
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V x ∑ w O j = Sgn ( j+ ji i + A
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neural nets in the fields mentioned
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where the first summation is over a
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circuit,” IEEE Trans. on Circuits
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their joint usage in many problems,
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1 0 1 0 11 0 1 0 1 0 1 1 0 10 1 1 1
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15.2 Deterministic Explanation of H
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Thus, in a total of N selections wi
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and population size = 2, which mean
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The behavior of GA without mutation
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a = ∑ Lt (π 0 P n ) i i=1 n→
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Eθ GA Program Z1, Z2, Z3, Z4, X1,
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e [W1 W2 W3 W4 W5 W6] T and [ G1 G2
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function. So, GA in each evolution
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f(x) = Sin (x) + [x * x + y] 1/2 ca
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(EQ (DU(MT CS) (NOT CS)) (DU(MS NN)
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[4] Chakraborty, U. K. and Muehlenb
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16 Realizing Cognition Using Fuzzy
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Cognitive maps are generally used f
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Theorem 16.1: With initial values o
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Here W T is a transposed weight mat
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example, for moving one’s arm, th
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and the weight adaptation equation
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Xk+1 ∆Wk = α Ek οXk+1 T / ((Xk+
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d5 d9 d1 d6 d7 d8 d10 d11 d1=Front
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16.10 Conclusions and Future Direct
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[6] Kosko, B., “Fuzzy cognitive m
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however, have a narrow spectrum of
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contaminated with it. However, for
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1. Move the mask over the image, so
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∇ 2 (g * f ) = ( ∇ 2 g ) * f. W
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It may be noted that segmenting an
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machine has to narrate the game onl
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schematic diagram, briefly outlinin
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same process for all clusters, we g
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Level 1 Level 2 Level 0 Neuron Fig.
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I (u, v) YI Fig. 17.12: Camera mode
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epipolar planes meet the image plan
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(a, b, 1) Fig. 17.15: A 3-D represe
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case III: Planes not parallel to th
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yi = -fi (xi,* ai - 1*) + ( fi / a
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Sample Execution: This is a program
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U t11 t12 t13 t14 x V = t21 t22 t23
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obtained after linearizing measurem
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co-ordinate systems. The correspond
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18 Linguistic Perception Building p
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psychological aspects of understand
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S NP VP ART N VP the man VP V NP ki
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( S ( NP ( ( ART the ) (N man ) ) (
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Sentence: NP VP 1 6 NP: ART N 2 ART
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18.2.3.1 Learning For adaptation of
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context sensitive grammar is thus m
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Generally, we start the sentence S
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VP: V NP S0 S1 Tagged procedure V:=
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Laugh agent animal enjoyer entity p
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18.5 Discourse and Pragmatic Analys
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Thus the elements of communicative
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19 Problem Solving by Constraint Sa
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The recognition problem is the pres
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CSP deals with two classical proble
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= 10 10 = 10 = * Fig. 19.2 (b): Pro
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+ _ V1 R1 V 2 V3 I1 I2 I3 V R2 R3 S
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V = Now assuming the values of V, R
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On (A, Ta) ∧ On (B, Ta) ∧On (C,
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We now represent the neighboring re
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Step 1: (x
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such variable xj , xk, etc., attach
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of C3. If the constraints are liste
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The possible labels of the junction
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The main part of CSP is the formula
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20 Acquisition of Knowledge Acquisi
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invite the experts to attend a meet
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B E A= test ?, B = test results, C
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The database in fig. 20.2 is extrac
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20.5 Knowledge Refinement by Hebbia
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* * * n i ( t + 1) = n i ( t ) at t
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L(r,s) L(s,r) Y(r) Y(s) OS(r,s) n1
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The FPN of fig. 20.5 is formed with
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L(a,l) L(l,a) Y(a) Y(l) OS(a,l) n1
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[3] Cooke, N. and Macdonald, J.,
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21 Validation, Verification and Mai
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Here the problem characteristic is
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The chapter will cover various issu
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21.2.1 Qualitative Methods for Perf
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Paired t-test: Suppose xi ∈ X and
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Ancestor P = {p1,p2} Tr = {tr1,tr2,
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21.3.2 Inconsistencies in Knowledge
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q tr1 tr2 p1 p2 …………… pn
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A rule may also include a number of
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21.4 Maintenance of Knowledge Based
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control of data and knowledge is un
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8. Stefik, M., Introduction to Know
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are not suitable for AI application
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
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EPN = { P, Tr, D, f, m, A, a, I, o
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It is to be noted that if- then ope
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After the bindings of the variables
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F(x) ← A(X) , B(Y) (1) A(1) ← (
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the result produced by clause (2) m
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Else Flag:= true; End; Until no-of
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transition for the PTVVM. The PTVVM
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For the sake of convenience, the pi
Page 678 and 679:
22.6 Conclusions The chapter starte
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Rule 3: S(X, Y) → Z (Y, X) Rule 4
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23 Case Study I: Building a System
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features in human faces and their r
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Definition 23.4: A linear edge segm
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lock containing edge. The productio
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Definition 23.13: The measure of di
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Partitioning Fe into Blocks Feature
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The fuzzy membership functions used
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∆ • Fig. 23.4: The delta and th
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Thus we have altogether 6 different
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cross-section of the vocal tract, w
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23.4.2 Training a Multi-layered Neu
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information with their normalized v
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SR (Y, X) OR (M (X) ∧ M (Y) ∧ L
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procedure, however, no attempts hav
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23.5.5 Belief Revision and Limitcyc
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that the inferences will be minimal
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the formation of the FPN. The FPN o
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is then initiated for detecting the
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initial fuzzy beliefs at all places
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at all feasible x, y. Then estimate
Page 722 and 723:
[13] Malmberg, B., Manual of Phonet
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24.1 Mobile Robots Mobile robots ar
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about its world. There exists ample
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the process, else it attempts to fi
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Depending on the type of planning p
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WEST NORTH SOUTH Fig. 24.5: Represe
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NW child B NE child 'C' SW child 'D
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As observed from the node status, t
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In their evolutionary planner algor
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tuning of the path, such as avoidin
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S S= starting point, G= Goal point,
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Once the training is over, the syst
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N o Table 24.2: Training pattern sa
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24.9.1 Finite State Machine Finite
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occurrence of a state, but also in
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24.10 An Application in a Soccer Pl
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Exercises 1. Devise an algorithm fo
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[15] Meng, H. and Picton, P. D.,
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24 + The Expectations from the Read
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Appendix A How to Run the Sample Pr
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Predicate: LSR Argument1: S Argumen
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ANTECEDENT 1: Predicate: END conclu
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Rules properly arranged MAIN MENU:
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Level POSITION_FROM_LEFT NODE 1 1 H
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calculating membership values enter
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C > File currently in progress = ci
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When the goal is within concave obs
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path selected 160,160 and 240,240 T
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(a) Robot entering the room (b) Aft
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where tr and Outr denote the target
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∂E/∂Wsp = ∑r (∂E/∂Outr) (
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Proof of theorem10.2: For an oscill
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Thus, we get analogously , and 1 0
Page 788:
= Q 'f m T o Rf m o ( Q ' f m o I )
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