Is there a (fork) symbol for probabilistic causality? Logic

Since it should be a connective, the type is \mathbin; then we can use TeX's rules for relations:

\documentclass{article}

\newcommand{\fork}{%
  \mathbin{%
    \supset
    \mathrel{\mkern-9mu}%
    \mathrel{-}%
  }%
}

\begin{document}

The connective for the fork is $\fork$
and we can write $a\fork b$ or also
$a\fork_u b$.

\end{document}

Choose the kerning based on your liking.

At its simplest, I propose a simple overlap of a \supset and a -, with a kern to effect the overlap. However, A Rmano notes, this may not have the proper spacing relative to adjacent material. Thus, if one wishes a general symbol, that works across math styles, I have provided here \fork.

EDITED for \mathbin instead of \mathrel.

\documentclass{article}
\usepackage{scalerel}
\newcommand\fork{\mathbin{\ThisStyle{{\supset}\kern-\dimexpr.5\LMex+3pt\relax{-}}}}
\begin{document}

$\supset\mkern-15mu-_\mathrm{u}$

$\fork_\mathrm{u}$
$\scriptstyle \fork_\mathrm{u}$
$\scriptscriptstyle \fork_\mathrm{u}$
\end{document}

Mnsymbol and Mdsymbol have \rightpitchfork glyphs (and indeed quite a few other pitchforks). Here is a way to use it, along with \leftpitchfork, without loading Mnsymbol. In addition , I defined an extensible version \xleftfork. They have bold versions.

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern, mathtools}

\DeclareFontFamily{U}  {MnSymbolA}{}
\DeclareSymbolFont{MnSyA}         {U}  {MnSymbolA}{m}{n}
\SetSymbolFont{MnSyA}       {bold}{U}  {MnSymbolA}{b}{n}
\DeclareFontShape{U}{MnSymbolA}{m}{n}{
<-6>  MnSymbolA5
<6-7>  MnSymbolA6
<7-8>  MnSymbolA7
<8-9>  MnSymbolA8
<9-10> MnSymbolA9
<10-12> MnSymbolA10
<12->   MnSymbolA12}{}
\DeclareFontShape{U}{MnSymbolA}{b}{n}{
<-6>  MnSymbolA-Bold5
<6-7>  MnSymbolA-Bold6
<7-8>  MnSymbolA-Bold7
<8-9>  MnSymbolA-Bold8
<9-10> MnSymbolA-Bold9
<10-12> MnSymbolA-Bold10
<12->   MnSymbolA-Bold12}{}

\makeatletter
\newcommand{\xleftfork}[2][]{%
\ext@arrow 0079\xleftforkfill@{#1}{#2}%
}
\newcommand{\xleftforkfill@}{%
\arrowfill@\Mnrelbar\Mnrelbar{\mathrel{\leftpitchfork}}
}
\newcommand{\xrightfork}[2][]{%
\ext@arrow 0097\xrightforkfill@{#1}{#2}%
}

\DeclareMathSymbol{\rightpitchfork}{\mathrel}{MnSyA}{"88}%
\DeclareMathSymbol{\leftpitchfork}{\mathrel}{MnSyA}{"8A}%
\DeclareMathSymbol{\Mnrelbar}{\mathrel}{MnSyA}{"D0}%

\begin{document}

$ A \rightpitchfork B\enspace B \leftpitchfork A$
\bigskip

\boldmath      $ A \rightpitchfork B\enspace B \leftpitchfork A$
\bigskip

$C \xleftfork{\text{an extensible pitchfork}}D$

\end{document}