CS621: Artificial Intelligence Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture–2: Introduction: Search+Logic

Logistics Faculty instructor: Dr. Pushpak Bhattacharyya ( TAs: Saurabh Anup Course home page Lectures mirrored at Venue: CSE Building: S9 1 hour lectures 3 times a week: Mon-9.30, Tue , Thu-11.30

Disciplines which form the core of AI- inner circle Fields which draw from these disciplines- outer circle. Planning Computer Vision NLP Expert Systems Robotics Search, Reasoning, Learning Knowledge- Representation

Search: Everywhere

Planning (a) which block to pick, (b) which to stack, (c) which to unstack, (d) whether to stack a block or (e) whether to unstack an already stacked block. These options have to be searched in order to arrive at the right sequence of actions. ACBA B C Table

Vision A search needs to be carried out to find which point in the image of L corresponds to which point in R. Naively carried out, this can become an O(n2) process where n is the number of points in the retinal images. World Two eye system RL

Robot Path Planning searching amongst the options of moving Left, Right, Up or Down. Additionally, each movement has an associated cost representing the relative difficulty of each movement. The search then will have to find the optimal, i.e., the least cost path. O1O1 R D O2O2 Robot Path

Natural Language Processing search among many combinations of parts of speech on the way to deciphering the meaning. This applies to every level of processing- syntax, semantics, pragmatics and discourse. The man would like to play. Noun Verb NounVerb Preposition

Expert Systems Search among rules, many of which can apply to a situation: If-conditions the infection is primary-bacteremia AND the site of the culture is one of the sterile sites AND the suspected portal of entry is the gastrointestinal tract THEN there is suggestive evidence (0.7) that infection is bacteroid (from MYCIN)

Search building blocks  State Space : Graph of states (Express constraints and parameters of the problem)  Operators : Transformations applied to the states.  Start state : S 0 (Search starts from here)  Goal state : {G} - Search terminates here.  Cost : Effort involved in using an operator.  Optimal path : Least cost path

Examples Problem 1 : 8 – puzzle S 2 G Tile movement represented as the movement of the blank space. Operators: L : Blank moves left R : Blank moves right U : Blank moves up D : Blank moves down C(L) = C(R) = C(U) = C(D) = 1

Problem 2: Missionaries and Cannibals Constraints The boat can carry at most 2 people On no bank should the cannibals outnumber the missionaries River R L Missionaries Cannibals boat Missionaries Cannibals

State : #M = Number of missionaries on bank L #C = Number of cannibals on bank L P = Position of the boat S0 = G = Operations M2 = Two missionaries take boat M1 = One missionary takes boat C2 = Two cannibals take boat C1 = One cannibal takes boat MC = One missionary and one cannibal takes boat

C2MC Partial search tree

Problem 3 BBWWW B G: States where no B is to the left of any W Operators: 1) A tile jumps over another tile into a blank tile with cost 2 2) A tile translates into a blank space with cost 1 All the three problems mentioned above are to be solved using A*

Power of Logic

Disciplines which form the core of AI- inner circle Fields which draw from these disciplines- outer circle. Planning Computer Vision NLP Expert Systems Robotics Search, Reasoning, Learning Knowledge- Representation

Circuit Verification Does the circuit meet the specs? Are there faults? are they locatable?

Example : 2-bit full adder C1X2X1YC X 1, X 2 : inputs; C 1 : prev. carry; C 2 : next carry; Y: output

K-Map x2x1 c1 Y 0 1

K-Map (contd..) x2x1 c1 0 1 C2

Circuit

Verification First task (most difficult)  Building blocks : predicates  Circuit observation : Assertion on terminals

Predicates & Functions Function–1signal(t)t is a terminal ; signal takes the value 0 or 1 Function–2type(x)x is a circuit element; type(x) takes the value AND, OR, NOT, XOR Predicate – 3connected(t1,t2)t1 is an output terminal and t2 is an input terminal Function-3In(n,x)n th input of ckt element x Function-4Out(x)Output of ckt element x

Alternate Full Adder Circuit

Functions type(X) : takes values AND, OR NOT and XOR, where X is a gate. in(n, X) : the value of signal at the n th input of gate X. out(X) : output of gate X. signal(t) : state at terminal t = 1/0 Predicates connected(t1,t2): true, if terminal t1 and t2 are connected

General Properties Commutativity: ∀ t 1,t 2 [connected(t 1,t 2 ) → connected(t 2,t 1 )] By definition of connection: ∀ t 1,t 2 [connected(t 1,t 2 ) → { signal(t 1 ) = signal(t 1 )}]

Gate properties 1. OR definition: 2. AND definition:

Gate properties contd… 1. XOR definition: 2. NOT definition:

Some necessary functions a. no_of_input(x), takes values from N. b. Count_ls(x), returns #1s in the input of X

Circuit specific properties Connectivity: connected(x 1, in(1,A 1 )), connected(x 2, in(2, A 1 )), connected(out(A 1 ), in(1, A 2 )), connected(c1, in(2, A 2 )), connected(y, out(A 2 )) … Circuit elements: type(A 1 ) = XOR, type(A 2 ) = XOR, type(A 3 ) = AND …

Topics to be covered (1/2) Search General Graph Search, A* Iterative Deepening, α-β pruning, probabilistic methods Logic Formal System Propositional Calculus, Predicate Calculus Knowledge Representation Predicate calculus, Semantic Net, Frame Script, Conceptual Dependency, Uncertainty

Topics to be covered (2/2) Neural Networks: Perceptrons, Back Propagation, Self Organization IR and AI Semantic Web and Agents Statistical Methods Markov Processes and Random Fields Computer Vision, NLP, Machine Learning Planning: Robotic Systems Confluence of NLP and CV: text and image based search Anthropomorphic Computing: Computational Humour, Computational Music

Resources Main Text: Artificial Intelligence: A Modern Approach by Russell & Norvik, Pearson, Other Main References: Principles of AI - Nilsson AI - Rich & Knight Knowledge Based Systems – Mark Stefik Journals AI, AI Magazine, IEEE Expert, Area Specific Journals e.g, Computational Linguistics Conferences IJCAI, AAAI

Allied Disciplines PhilosophyKnowledge Rep., Logic, Foundation of AI (is AI possible?) MathsSearch, Analysis of search algos, logic EconomicsExpert Systems, Decision Theory, Principles of Rational Behavior PsychologyBehavioristic insights into AI programs Brain ScienceLearning, Neural Nets PhysicsLearning, Information Theory & AI, Entropy, Robotics Computer Sc. & Engg.Systems for AI

Evaluation (i) Exams Midsem Endsem Class test (ii) Study Seminar (iii) Work Assignments