ARTIFICIAL INTELLIGENCE CS 621 Artificial Intelligence Lecture 32

AI A* Language processing Predicate calculus Computer vision Search, Reasoning, Learning, Knowledge rep. robotics

Planning • Planning ( classical planning) – Hierarchical planning – Probabilistic planning • Problem

0 on(C, A) 1 clear(C) 1 hand empty unstack(C, A) holding(C) 2 C A

S 0 : pickup(x) x=B handempty clear(C) on(C, A), clear(B) on(B, table) on(A, table)

Backward Chaining Pickup(x) Putdown(x) Unstack(x, y) Stack(x, y) 28 -10 -05 Goal state On(A,

Decision to apply forward or backward chaining depends on precision of goal, fan-out factor,

Definition of Kernel ith kernel : the matrix with i columns and covering the

Exercise How resilient is the triangular table? Will the robot always be failsafe if

Mutual Information MI on the noisy channel. A b 1 b 2. . bm

Discussion on MI - 1 Probability distribution on A pi = prob of sending

Discussion on MI - 2 Mutual Information I(A, B) is the reduction in uncertainty

Discussion on MI - 3 Prove that I(A, B) > = 0 Apply the

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ARTIFICIAL INTELLIGENCE CS 621 Artificial Intelligence Lecture 32 - 28/10/05 Prof. Pushpak Bhattacharyya Planning contd. , Mutual Information etc. 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 1

AI A* Language processing Predicate calculus Computer vision Search, Reasoning, Learning, Knowledge rep. robotics Neural net, Clustering, PAC learning 28 -10 -05 Predicate logic, Fuzzy logic Expert sys Formal systems + soundness Completeness consistency Forward + backward chaining Prof. Pushpak Bhattacharyya, IIT Bombay 2

Planning • Planning ( classical planning) – Hierarchical planning – Probabilistic planning • Problem – blocks world – Rules – S 0 – Goal 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 3

0 on(C, A) 1 clear(C) 1 hand empty unstack(C, A) holding(C) 2 C A 2 A B C B START putdown(C) GOAL 3 3 on(B, table) Clear(B) hand empty pickup(B) 4 clear(C) 4 holding(B) stack(B, C) 5 5 on(A, table) clear(A) hand empty pickup(A) 6 6 clear(B) on(B, C) 7 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay holding(A) stack(A, B) on(A, B) 4

S 0 : pickup(x) x=B handempty clear(C) on(C, A), clear(B) on(B, table) on(A, table) Clear(C) On(C, A), on(A, table) Holding (B) 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay unstack(c) unstack(C) holding(C) clear(B) on(B, table) on(A, table) clear(A) 5

Backward Chaining Pickup(x) Putdown(x) Unstack(x, y) Stack(x, y) 28 -10 -05 Goal state On(A, B) On(B, C) On(C, table) Handempty Clear(A) Prof. Pushpak Bhattacharyya, IIT Bombay Rules are applied backward 6

Decision to apply forward or backward chaining depends on precision of goal, fan-out factor, number of operators used. Resilience of the plan, fault tolerance, triangular table, kernel. 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 7

Definition of Kernel ith kernel : the matrix with i columns and covering the rectangle above the last row. 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 8

Exercise How resilient is the triangular table? Will the robot always be failsafe if its operation is guided by triangular table? Kernel-i captures the state of the world when op(i) is about to be applied 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 9

Mutual Information MI on the noisy channel. A b 1 b 2. . bm a 1 a 2. . am B Noisy Channel 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 10

Discussion on MI - 1 Probability distribution on A pi = prob of sending ai qj = prob of receiving bj E(A) = pi log 1/pi m E(B) = qj log 1/qj n 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 11

Discussion on MI - 2 Mutual Information I(A, B) is the reduction in uncertainty of A having obtained info on B. I(A, B) = E(A) – E(A|B) Definition You can show, I(A, B) = E(A) + E(B) – E(A, B) 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 12

Discussion on MI - 3 Prove that I(A, B) > = 0 Apply the lemma xi log 1/xi <= xi log 1/yi where xi = yi = 1, i. e. xi & yi are probability distributions 28 -10 -05 Prof. Pushpak Bhattacharyya, IIT Bombay 13