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

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

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

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Unifiers

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

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

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

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

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

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

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

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

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