Standard logic uses simple facts and rules abiut a single situation. For example, the classic "Socrates is a man; all men are mortal, therefore Socrates is mortal". This example includes named things (Socrates), predicates (properties of things, such as "is a man"), of propositions (facts such as "Socrates is a man"), quantifiers (ways talking about lots of things at once, such as "all") and syllogisms (reasoning). These are often written in formal terms such as:
is_a_man(Socrates)
∀ p : is_a_man(p) ⇒ mortal(p)
mortal(Socrates) -- from the rule ( ∀ x : P(x) & Implies; Q(x) ) and P(y) infer Q(y)
Note how there are two levels of implication here the implies in the propositions (⇒ ) and the rule implication. The former that can be regarded as a syntactic sugar for the equivaent ands and ors:
X ⇒ Y. ≡ ¬ X ∨ Y
Standard logics can be contrasted with non-standard logic such as non-monotonic reasoning, modal logic or fuzzy logic
Used on pages 38, 40, 44, 45
Also known as standard