8.1 Representation Revisited

Desirable characteristics:

• Declarative (separates knowledge from inference)
• Compositional
• Context Independent
• Conciseness
• Unambiguous
• Expressive

8.2 Syntax and Semantics of First Order Logic

• Constant Symbols, e.g. Cs436
• Predicate Symbols, e.g. Evenp
• Function Symbols, e.g. Add-one
• Variables, e.g. x
• Universal Quantifier, ∀
• Existential Quantifier, ∃

Try exercise 8.6 to practice representing English sentences in First Order Logic.

• Some students took French in Spring 2001.
• Every student who takes French passes it.
• Try the others on your own!

Proofs

1. Represent English sentences in First Order Logic.
2. Convert the First Order Logic to CNF.
3. Negate the theorem being proved and convert this to CNF.
4. Use resolution theorem proving to find a contradiction.

Example

• Fact: CS 223 is a pre-requisite for CS 436.
• Fact: CS 221 is a pre-requisite for CS 223.
• Rule: If course x is a pre-requisite for course y and course y is a pre-requisite for course z, then course x is a pre-requisite for course z.
• Proof 1: CS 221 is a pre-requisite for CS 436.
• Proof 2: Find a pre-requisite for CS 436.