I came across the notation
$\renewcommand{vec}[1]{\mathbf{#1}}$
$$\text{flow}(\vec{x},\vec{y},t) \equiv \bigwedge_{j=1}^{n} \exists \vec{z}\in I : y_j-x_j = t\cdot f_j(\vec{z}).$$
equation when reading the paper Light-weight hybrid model checking facilitating online prediction of temporal properties in preparation for my master's thesis, but I have never seen the triangle symbol (with the $n$ on top) in front of the right hand side before.
Can someone tell me what it does or at least what it is called so I know what to look for myself? It reminds me of the intersection operator, but that one should be round, right? Or is this an alternative way of writing it?
Best Answer
The general formatting of " $X_{y=n_1}^{n_2}\;Z$ " pretty strongly implies "Make a bunch of expressions by replacing $y$ with each of the values from $n_1$ to $n_2$ in $Z$, and then combing those statements using $X$". This is the general pattern of $\Sigma$, $\Pi$, $\bigcap$, etc. I guess the word for it would be "n-ary $X$". There are variations and details that aren't in question here.
In this case, the "$Z$" is an $\exists$ statement; depending on the context you might call that a boolean, or a predicate, or a "statement", but in any case it's consistent with $⋀$ being logical conjunction, as suggested by Tyma Gaidash and Antares in the comments.
I can't definitively rule out an "exterior product" or "wedge product", but neither of them sound like they'd apply to existence expressions.