Logic

\vee, \lor \wedge \colon \oplus \otimes \lnot \forall \exists

Formal Notation

Inference: agent will use knowledge and logic to provide inference
Soundness: Only valid conclusions can be proven
Completeness: All valid conclusions can be proven
Predicate: a function that maps object args to T/F
- Feathers(bluebird) >>> True

Implication x implies y, $\Rightarrow$

if an animal lays eggs and an animal flies than the animal is a bird

\text{If Lays-eggs(animal)} \wedge \text{Flies(animal)} \Rightarrow \text{Then Bird(animal)}

if an animal lays eggs or an animal flies than the animal is a bird

\text{Lays-eggs(animal)} \vee \text{Flies(animal)} \Rightarrow \text{Then Bird(animal)}

If an animal flies and is not a bird, it is a bat

\text{Flies(animal)} \wedge \lnot\text{Bird(animal)} \Rightarrow \text{Bat(animal)}

Demorgan's law $\lnot(A\wedge B) == \lnot A \vee \lnot B$
- The outer not flips the inner operation

Kinda weird logic for "Implies" $\Rightarrow$

$A \Rightarrow B == \lnot A \vee B$

Prove the opposite of what we're trying to prove
Start by eliminating the thing you're trying to prove with the contrapositive in the full sentence