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Robert Laing's programing notes

Logic

By Robert Laing

Stephen Cole Kleene Mathematical Logic

prime formulas or atoms
Denoted by capital Roman letters from late in the alphabet, as P, Q, R, …, P1, P2, P3, …
composite formulas or molecules
These consist of five rules.
  1. Equivalence ⇔, ≡, ↔, ~
  2. Implication ⇒, →, ⊃
  3. Conjuction ∧, ·, & , “,”, ‘and’
  4. Disjunction ∨, |, “;”, ‘or’
  5. Negation ¬, ˜, !, “+”, ‘not’

The above order is the precedence.

Truth Tables

A B A ⇔ B A ⇒ B A ∧ B A ∨ B ¬A
t t t t t t f
t f f f f t f
f t f t f t t
f f t t f f t

Critics of implication include Clarence Irving Lewis and it doesn’t come up much in logical programing.

Aristotle rules of inference

Last updated on 12 Jan 2021
Published on 12 Jan 2021

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