# Frontier Software

Robert Laing's programing notes

# Logic

By Robert Laing

file:///home/roblaing/ebooks/LogicForProblemSolving.pdf

resolution rule

convert from standard from to clausal form

# Logic

30/50

http://infolab.stanford.edu/~ullman/focs/ch12.pdf

## DeMorgan’s Laws

¬(p ∧ q) ⇔ ¬p ∨ ¬q ¬(p ∨ q) ⇔ ¬p ∧ ¬q

Truth tables 12.4

Converting truth tables to logical expressions 12.5

Karnaugh maps 12.6

Logical expressions 12.7, 12.8

Common proof techniques 12.9

Deduction 12.10

Resolution 12.11

# Sets

http://infolab.stanford.edu/~ullman/focs/ch07.pdf

Stephen Cole Kleene Mathematical Logic

Kleene star

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 (bottom up, with ¬ highest).

I’m opting for the same choice of symbols as

## 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
preclusion
Possibly a better name for A ⇒ B than implication is preclusion. ¬A ∨ B gives the same truth table

Logic textbooks, eg Clarence Irving Lewis,

created a distinction between what is generally thought of as implication and the odd truth table version. Furthermore, A ⇒ B can be substituted with ¬A ∨ B.

Similarly A ⇔ B can be substituted (A ∧ B) ∨ (¬A ∧ ¬B), so ¬, ∨, ∧ are all we really need.

Aristotle rules of inference