Week 1 Knowledge

• Propositional Symbols


  Represent facts/statements. Example: 'it's raining' = R
• Logical Connectors:

  ¬ = not

  ^ = and

  v = or

  -> = implication (if a True, b True. if b True, a True or False)

  <-> = biconditional (if a True, b True. if b True, a True)
• Model: A possible world, assigning a truth value to every propositional symbol. Example: {R = true, T = false}
• Knowledge Base: a database containing every known fact.
• Entailment: in every possible world, if b is True then a must be True. a⊢b
• Inference Rule #1

  Modus Porsens

  is a implies b and a is True, then b is True

  
• Inference Rule #2

  And Elimination

  if a is True and b is True, then a must be True

  
• Inference Rule #3

  Double Negation Elimination

  if not not a, then a (must be True)

  
• Inference Rule #4

  Implication Elimination

  if a implies b, then either a isn't True (and thus b is False) or a is True (and thus B is True)

  
• Implication Rule #5

  De Morgan's Law

  ver 1: if not a and b True, either a isn't True or b isn't True

  ver 2: if not a or b True, both must not be True

  
• Inference Rule #6

  Distributive Property

  if a is True and, either b is True or c is True

  then either a and b are True or a and c are True

  
• THEOREM PROVING: uses same logic as search method.

  Initial State: starting knowledge base

  Actions: inference rules

  Transition Model: new knowledge base, after inferences

  Goal Test: statement to prove

  Path Cost Function: number of steps in the proof
• Clause: propositional symbols connected by 'or's

  
• Conjunctive Normal Form: clauses connected by 'and's

  
• Empty Clause: Equivalent to False and can be used in resolution.

  Example: To prove b entails a, test for b is True and a is not True until the empty clause is found.
• Example of First-Order-Logic

  
• Universal Quantification: something that's True for all values of a variable.

  
• Existential Q: something that's True for some values of a variable.