# Why Continue Using Logic Symbology and Truth Tables

With the advent of computers and the creation and adoption of so many computer programming languages, are logic symbols still valuable or are they a relic of the past?

If logic symbology remains relevant and valuable, can you give an example?

• Why teach kids how to count, calculators are readily available. Let's get more people who not only can not balance their checkbooks, but can not put two premises together and draw a conclusion also. Commented Jun 19, 2015 at 2:59
• Modern computing languages use different symbols for typographical and typeability reasons but track those as closely as possible. We write little implies symbols => or ->, & or && for and's, | or || for or's, { a <- A: P(a) } <= { b <- A: Q(b) } is not uncommon in testing code for some languages. Children of Prolog even have little turnstyles :- to mark deduction rules.
– user9166
Commented Jun 19, 2015 at 18:58
• I don't understand your reasoning behind contrasting logical symbols and programming languages. Considerations in formal logic is exactly what led to the invention of programming languages in the 20's and 30's (or the discovery of their possibility) and the language of logic serves another, maybe even broader purpose. Moreover, the two overlap in the Curry–Howard correspondence. tl;dr the question is odd, what's your background? Commented Jun 23, 2015 at 8:12

1. Logic symbols are extensively used, especially in programming languages. As a random example I have been working with lately, this 2014 paper featuring a new block cipher shows this very well in appendix H:

``````; Linear Layer and Inverse Linear Layer: L0
movw t0, s0 ; t1:t0 = s1:s0
swap s0
swap s1
eor s0, s1
eor t0, s0
mov s1, t0
eor s0, t1
``````

`eor` means 'exclusive or', so out of 7 instructions here, 3 use a logical operation. And this is not just something that happens in assembly. My Python implementation of the same cipher uses logic intensively as well.

But also think of bitmasks and other uses of logic in computing science.

2. Logic teaches you to think, and to reason precisely and correctly. It teaches you to recognise hidden assumptions. All this is incredibly useful in different fields - philosophy, but also science.

Boolean algebra is a subset of logic symbols and they are used a lot in computer languages. So the advent of computers have made logic more relevant, not less.

If you want to talk about logic versus computer science, how about computational complexity, which was basically founded by logicians?

• Determining whether or not a logical formula is a tautology is the most famous problem in coNP, which is to say that it is a problem immediately relevant to the P vs. NP problem, whose resolution would win a million-dollar from the Clay Institute (as well as international fame and a place alongside Turing and Boole in the annals of logic and computer science).

• Logical operations are the very starting point of circuit complexity, which is the most promising direction to seek provable big-picture results in computational complexity, and — speaking of modern computing technology — is also one of the easiest gateways to the formalism of quantum computation.

Now, if you'd rather focus on the necessity of the symbology: technically you might not need it — but would you teach algebra without arithmetic symbols? The symbology of logic is nothing more or less than an efficient notation — albeit one without which you can accomplish very little in practise except muse deeply about the square of syllogisms a la scholastic philosophers.