What is the reason for different typographical symbols for logical operators?

Question

I thought that ∧ is a standard symbol for logical conjunction used in textbooks. I understand that many typographically restricted environments, e.g. programming languages, will substitute it with: &, and, etc. I've noticed that books about Description Logic are using Π symbol for conjunction instead of ∧. Similarily with ∨ vs. ⊔. What is the reason?

Answer 1

It is for the same reason as for any symbolic system: there are different communities that each developed their own language. Not everyone in the world speaks English, and indeed there is no one natural language spoken by everyone in the world.

With natural languages there are clear geographic reasons for this happening, but for later symbol systems used in math and science communities were formed in more abstract ways. So it is not as if every single individual just makes up their own language … that is unsustainable (I vaguely remember reading somewhere that linguistic anthropologists found that it takes something like 100 people to sustain a natural language … but please don’t hold me to that…) and of course would not work as a way to communicate with others. But it is also not true that everyone is part of the same one and single community.

The situation is similar to the lack of a single standard for which side of the road to drive on, or the fact that many countries are still not adopting the metric standards.

Also note that each community may have a different focus, perspective, or practical purpose for their symbol systems, even if the different communities talk about what is basically the same thing. In fact, depending on that context, perspective or purpose I myself may find one set of symbols preferable over another. For example, when I use logic to analyze arguments, I’ll use expressions like $P \land \neg Q$, for that can still be directly read and understood as the English ‘$P$ and not $Q$’, but when I use logic to analyze computer circuitry I’ll use $PQ’$, because that is easier and faster to algebraically work with. And people doing description logics may have their practical reasons for using a different notation yet.