2.1 Formalization

To formalize means writing an expression in a standard form which anyone can understand.

When working with logical algorithms, you can be thinking all the time in phrases like ``If I have a LCD screen but it has too many dead pixels, then I need another monitor''. You can, but they are too long. It's better to represent each action with a letter, and write the phrase using such letters along with simple words like and, or, not, or then.

For example, we have this vocabulary:

$L$: have a LCD (Liquid Crystal Display) monitor

$P$: have all pixels working perfectly, with not too many fused ones

$M$: need a new monitor

The phrase ``If I have a LCD screen but it has too many dead pixels, then I need another monitor'' is better expressed by ``if $L$ and not $P$, then $M$''.

At natural deduction we will only use the version with letters, following these conditions:

• The letters (named propositional letters) are uppercase.
• Normally $P$, $Q$, $R$, $S$, ... are used, but anyone else is allowed.
• We use some special symbols for the operators and, or, not and implication.