Unit 13+14+15: Logic

Structure of Simple Propositions

A simple proposition consists of one predicator (written in CAPITALS) and one or more arguments (written in lower-case letters).

E.g: "John loves Mary" → j LOVE m.

Identity Predicate

In equative sentences, the verb be represents the identity predicate, symbolized by =

E.g: "Clark Kent is Superman" → ck = s.

Conjunction

Corresponds to English and (and but). A conjunction p & q is true only if both p and q are true.

E.g: "John is tall and Mary is small" → (j TALL) & (m SMALL).

Disjunction

Corresponds to English or. A disjunction p V q is true if at least one of the propositions is true.

E.g: "Harry is here or Bill is away" → (h HERE) V (b AWAY).

Negation

Corresponds to English not. It reverses the truth value of a proposition

E.g: "Alice didn't sleep" → ~ a SLEEP

Implication/Conditional

Corresponds to if... then. It is used in rules like Modus Ponens (if p, then q; p is true; therefore q is true)

E.g: "If it rains, the ground gets wet" → i RAIN → g WET

Equivalence/Biconditional

Corresponds to if and only if. It asserts that two propositions always have the same truth value. (Phép tương đương - ≡ hoặc ↔)

John is Tom’s father if and only if Tom is John’s child.

j FATHER t = t CHILD j

De Morgan’s Laws

Phủ định của một phép tuyển bằng phép hội của các phủ định

E.g: Neither Alice nor Bill came" → phủ định của Either Alice or Bill come ~ (a COME V b COME) hoặc (~ a COME) & (~ b COME)