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?

  • 3
    $\begingroup$ It may mean $a_1$ and $a_2$ and $\dots$ and $a_j$ $\endgroup$ Mar 23 at 15:44
  • 6
    $\begingroup$ It looks like conjunction to me. $\bigwedge_{j=1}^n\phi_j=\phi_1\wedge\ldots\wedge \phi_n$ $\endgroup$
    – Antares
    Mar 23 at 15:45

1 Answer 1


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.


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