Monotonicity

• What we've described so far is First Order Predicate Logic (FOPL).
• Once a fact is in, you can't take it out.
• That is, the system only gets more information. It is monotonic.
• If you have a fact, you can use that fact to derive new facts.
• If you take that fact away, how can you remove all of the facts that you derived.
• The system also needs to be consistent. You can't have X and -X. If you do, you can derive any fact.
• For example, if we have contradictory facts, we can derive pigs fly.
• Let's have A be pigsFly(y), which you can expand.
• You know X (e.g. bestTeacher(Chris)) and -X(-bestTeacher(Chris))
• You know False->A is True for any value of A, and X and -X is False for any value of X.
• So X and -X -> A, and A is true.
• You need consistency.