BUSS 925: Techniques for Knowledge-Based Systems Development

Exercises for practice:

• Translate each of the following into both conjunctive and disjunctive normal form. Both these problems are considerably more complex than what you would face in an exam setting, but if you can solve these, you can solve them all...(A hint for getting more practice with such problems: Write down any arbitrary sentence in propositional logic which is syntactically correct, then transform into the two normal forms.)
  • ((P AND Q) OR (P OR (NOT Q))) IMPLIES ((P OR (NOT R)) AND S)
  • (((NOT P) OR Q) AND (P AND (NOT Q))) IMPLIES ((P AND R) OR (NOT S))
• Translate the following sentence into predicate logic:
  • Every programmer except John is smart.
  • There is exactly one smart programmer besides John.
  You may only use the following predicates:
  • equal(x,y), used to denote x=y.
  • programmer(x), used to denote that x is a programmer.
  • smart(x), used to denote that x is smart.