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In a paper, I found the following definition: definition found in the paper

I'm looking for the first sign, the OCR program failed to recognize. It's something like a combination of a \vdash and a \sim. I tried Detexify, but failed to find the correct symbol.

Does this symbol exists in LaTeX, or can I generate such symbol (for instance by adding a description in METAFONT?)

Somewhere further in the paper, the negation of that symbol also appears: the same symbol but with a diagonal line.

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Mostly such symbols (eg \models) are constructed from other symbols anyway so if you don't find it in a font ready built you can copy the models definition:

enter image description here

\documentclass{article}
% \DeclareRobustCommand
%  \models{\mathrel{|}\joinrel\Relbar}


\DeclareRobustCommand
  \sv{\mathrel{|}\joinrel\mathrel{\smash{\sim}}}

\begin{document}

$A\models B$

$X \sv Y$

\end{document}

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