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CS344: Artificial Intelligence

CS344: Artificial Intelligence. Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture 20,21: Application of Predicate Calculus. Application of Predicate Calculus. Systematic Inferencing. Knowledge Representation. Puzzles. -- Circuit Verification - Robotics - Intelligent DB.

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CS344: Artificial Intelligence

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  1. CS344: Artificial Intelligence Pushpak BhattacharyyaCSE Dept., IIT Bombay Lecture 20,21: Application of Predicate Calculus

  2. Application of Predicate Calculus Systematic Inferencing Knowledge Representation Puzzles • -- Circuit Verification • - Robotics • - Intelligent DB

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

  4. Example : 2-bit full adder X1, X2: inputs; C1: prev. carry; C2: next carry; Y: output

  5. K-Map Y x2x1 00 01 10 11 c1 0 1

  6. K-Map (contd..) C2 x2x1 00 01 10 11 c1 0 1

  7. Circuit

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

  9. Predicates & Functions

  10. Alternate Full Adder Circuit

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

  12. General Properties • Commutativity: ∀t1,t2 [connected(t1,t2) → connected(t2,t1)] • By definition of connection: ∀t1,t2 [connected(t1,t2) → { signal(t1) = signal(t1)}]

  13. Gate properties • OR definition: • AND definition:

  14. Gate properties contd… • XOR definition: • NOT definition:

  15. Some necessary functions no_of_input(x), takes values from N. Count_ls(x), returns #ls in the input of X

  16. Circuit specific properties • Connectivity: connected(x1, in(1,A1)), connected(x1, in(2, A1)), connected(out(A1), in(1, A2)) , connected(c1, in(2, A2)), connected(y, out(A2)) … • Circuit elements: type(A1) = XOR, type(A2) = XOR, type(A3) = AND …

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