What is logic?
A formal language that allows us to make assertions about the world in a precise way.
What are the two parts of AI logic?
- Knowledge-base: what the agent knows about the world, represented as “sentences” in written in the language of logic. However, not that in this course we’re much more interested in CONCEPTUAL knowledge, so we’ll focus much less on rigorous logical analysis
- Inference Engine (rules of inference): Applies rules of inference to the knowledge that the agent has.
What are the two parts of the rules for inference in an AI agent’s inference engine?
- Soundness: only valid conclusions can be proven
2. Completeness: All valid conclusions can be proven
What is a logical ‘predicate’?
A function that maps object arguments to True or False values.
What is an ‘implicative’ style construction of a logical predicate?
IF Feathers(animal): ---> True Then Bird(Animal) ---> True
The there is only one object (the animal) in this logical sentence, but two predicates. The : symbol is what is specifying the implication, namely, that if it is True that an animal has feathers, then it naturally follows that is the animal a bird also evaluates to True.
What does the ^ logical symbol mean?
The conjuction AND
What does the logical symbol v mean?
The disjunction OR
What does the logical symbol =) mean?
Implies/implication. Also used in same role in the lectures is the colon : (seems to be used interchangeably in lectures)
Does the commutative property hold for logical AND/OR operations?
Yes, e.g. A ^ B == B ^ A
Does the distributive property hold for logical AND/OR operations?
Yes, e.g. A ^ (B v C) == (A ^ B) v (A ^ C)
Does the associative property hold for logical AND/OR operations?
Yes, we can change parentheses and it doesn’t change anything, e.g. A v (B v C) == (A v B) v C
Logical sentences are monolithic - they cannot be re-written in a different form to make an inference easier? (True/False)
False, logical sentences CAN be re-written. See video on De Morgan’s Law, for example.
What is “Modus Ponens” and “Modus Tollens”
This one is a little complicated. Modus Ponens would, for example, allow an agent with the bootstrapped knowledge that feathers –> bird so that if it finds an animal somewhere with feathers, it can make the logical inference that animal is also a bird. The contrapositive is basically the opposite inference of this: if the agent finds an animal that DOESN’T have feathers, it can infer that it is NOT a bird.
TODO: Pickup on Logi_A Simple Proof video
TODO
