Drawing a vertical line between labels and items when using enumitem

Question

I am using the description environment of the enumitem package. I want to draw a long vertical line between the labels and the items. For instance, the result would be like

This example is drawn by using the tabularx package, which is not quite convenient for this use. The code is

\documentclass{article}

\usepackage{tabularx}

\newcommand{\prol}{\textsf{PL}}
\newcommand{\fol}{\textsf{FOL}}
\newcommand{\wff}{\textsf{wff}}
\newcommand{\ltrue}{\textsf{T}}
\newcommand{\lfalse}{\textsf{F}}

\begin{document}

\renewcommand{\arraystretch}{1.2}
\begin{tabularx}{\textwidth}{r|X}
Sentence & A sentence (also closed formula or ground formula) in logic refer to a declarative sentence that is either \ltrue{} or \lfalse{}. In \prol{}, 1) an atomic sentence have multiple constants and a single predicate; and 2) a compound sentence is formed by multiple atomic sentences combined by truth-functional connectives. In \fol{}, a sentence is a \wff{} with no free variables. A sentence can be viewed as expressing a proposition, something that must be \ltrue{} or \lfalse{}. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values. An atomic sentence is a sentence that has two or more logical subjects (constants) and a single predicate.\\

Claim & = Proposition\\

Proposition & A proposition is a particular kind of declarative sentence that affirms or denies a predicate of a subject. A proposition is either \ltrue{} or \lfalse{}.
\end{tabularx}

\end{document}

The line must persist on page change. I could not find a built-in function related to this in the user manual.

Answer 1

With tikzmark:

\documentclass{article}
\usepackage{enumitem}
\usepackage{tikZ}
\usetikzlibrary{tikzmark}

\newcommand{\prol}{\textsf{PL}}
\newcommand{\fol}{\textsf{FOL}}
\newcommand{\wff}{\textsf{wff}}
\newcommand{\ltrue}{\textsf{T}}
\newcommand{\lfalse}{\textsf{F}}

\begin{document}
    \begin{description}[align=right, labelsep=2em, leftmargin=\labelsep]
\item[Sentence] 
    \tikzmarknode{A}{A} sentence (also closed formula or ground formula) in logic refer to a declarative sentence  that is either \ltrue{} or \lfalse{}. In \prol{}, 1) an atomic sentence have multiple  constants and a single predicate; and 2) a compound sentence is formed by multiple atomic  sentences combined by truth-functional connectives. In \fol{}, a sentence is a \wff{} with no free variables. A sentence can be viewed as expressing a proposition, something that must be \ltrue{} or \lfalse{}. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values. An atomic sentence is a sentence that has two or more logical subjects (constants) and a single predicate.

\item[Claim]
    = Proposition

\item[Proposition]
    A proposition is a particular kind of declarative sentence that affirms or denies a predicate of a subject. A proposition is either \ltrue{} or \tikzmarknode{B}{\lfalse{}}.
\begin{tikzpicture}[overlay,remember picture,
                        ]
\draw[transform canvas={xshift=-1em}] (A.north west) -- (A.west |- B.south);
\end{tikzpicture}
    \end{description}
\end{document}

After (at least) two compilation you will get: