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UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering CSCE 580 Artificial Intelligence Ch.12 [P]: Individuals and Relations Proofs.

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Presentation on theme: "UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering CSCE 580 Artificial Intelligence Ch.12 [P]: Individuals and Relations Proofs."— Presentation transcript:

1 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering CSCE 580 Artificial Intelligence Ch.12 [P]: Individuals and Relations Proofs and Functions Fall 2009 Marco Valtorta mgv@cse.sc.edu

2 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Acknowledgment The slides are based on [AIMA] and other sources, including other fine textbooks David Poole, Alan Mackworth, and Randy Goebel. Computational Intelligence: A Logical Approach. Oxford, 1998 –A second edition (by Poole and Mackworth) is under development. Dr. Poole allowed us to use a draft of it in this course Ivan Bratko. Prolog Programming for Artificial Intelligence, Third Edition. Addison-Wesley, 2001 –The fourth edition is under development George F. Luger. Artificial Intelligence: Structures and Strategies for Complex Problem Solving, Sixth Edition. Addison-Welsey, 2009

3 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Instances and substitutions

4 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Unifiers

5 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Bottom-up procedure

6 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Ground instances and Herbrand interpretations

7 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Top-down procedure: SLD resolution with variables

8 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Top-down procedure (simplified)

9 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Top-down Procedure (Fig.12.3[P])

10 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Example of top-down derivation

11 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Another example (Ex.12.22[P])

12 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Function Symbols

13 UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Example: lists


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