0

Just like $\Sigma$ and $\Pi$ are the "big operators" for summation and multiplication, what would such operators be for logical operations? For example, would $\bigwedge\limits_{i} b_i$ be the logical-and operator applied on the set of booleans $b_i$? For some reason, although LaTeX does have \sum, there does not seem to exist any \And or \Or.

Tfovid
  • 153
  • There is \bigvee $\bigvee$ and \bigwedge $\bigwedge$ – is this a mathematical question or a question about LaTeX? – Martin R Nov 15 '22 at 09:50
  • @MartinR It's a mathematical question, but since I'll eventually need to write down what I'm talking about, I'd naturally like to also know how to do so in LaTeX. – Tfovid Nov 15 '22 at 09:52
  • Your guesses about the meanings of $\bigwedge_i,,\bigvee_i$ are correct, but note that if $\bot,,\top$ are respectively labelled $0,,1$ then $\bigwedge$ is equivalent to $\prod$. – J.G. Nov 15 '22 at 11:04

1 Answers1

-1

In first order logic "operators" are predicates.

you may have a formula: $(\forall x)(\exists y)(xPy)$

$P$ is a predicate and $x,y$ are the bound variables.

a predicate can be $n-$ary which can be interpreted in a suitable domain of discourse.

In the example above $P$ is a binary predicate, i.e. it acts on two variables.

ryaron
  • 1,091
  • So you mean the and operator $\land$ can't possibly by applied to a set (or more than two operands)? How does one represent an "and" operation on more than two booleans? – Tfovid Nov 15 '22 at 09:54
  • The $\land$ is not an operator, it is a connective. – ryaron Nov 15 '22 at 11:55