1. Dr. Mustafa Jarrar [email_address] www.jarrar.info University of Birzeit Chapter 8 First Order Logic Advanced Artificial Intelligence (SCOM7341) Lecture Notes University of Birzeit 2 nd Semester, 2010

7. b c a d e Objects: How do you conceptualize this World {a, b, c, d, e} Relations: On: {<a,b>, <b,c>, <d,e>} Above: {<a,b>,<b,c>,<d,e>} Clear: {<a>,<d>} Table: {<c>,<e>} Functions: Hat: {<b,a>, <c,b>, <e,d>,}

8. b c a d e Conceptualization How do you conceptualize this World < {a, b, c, d, e} {<a,b>, <b,c>, <d,e>} {<a,b>,<b,c>,<d,e>} {<a>,<d>} {<c>,<e>} {<b,a>, <c,b>, <e,d>,} > There can be other conceptualizations of the same world! = < Objects, Relations, Functions> Examples in science? e.g., light is a wave or particles, Examples in politics?

9. b c a d e How do you conceptualize this World < {a, b, c, d, e} {<a,b>, (b,c>, <d,e>} {<a,b>,<b,c>,<d,e>} {<a>,<d>} {<c>,<e>} {<b,a>, <c,b>, <e,d>,} > Conceptualization = Formalization of the above conceptualization may include :  x  y On(x,y)  Above(x,y)  x Clear(x)  Table(x) … ..

14. Models for FOL: Example

28. Equivalences