  We study an extension of $\mtl$ in pointwise time with rational expression
guarded modality $\reg_I(\re)$ where $\re$ is a rational expression over
subformulae. We study the decidability and expressiveness of this extension
($\mtl$+$\varphi \ureg_{I, \re} \varphi$+$\reg_{I,\re}\varphi$), called
$\regmtl$, as well as its fragment $\sfmtl$ where only star-free rational
expressions are allowed. Using the technique of temporal projections, we show
that $\regmtl$ has decidable satisfiability by giving an equisatisfiable
reduction to $\mtl$. We also identify a subclass $\mitl+\ureg$ of $\regmtl$ for
which our equi-satisfiable reduction gives rise to formulae of $\mitl$,
yielding elementary decidability. As our second main result, we show a tight
automaton-logic connection between $\sfmtl$ and partially ordered (or very
weak) 1-clock alternating timed automata.
