  In the last decades much research effort has been devoted to extending the
success of model checking from the traditional field of finite state machines
and various versions of temporal logics to suitable subclasses of context-free
languages and appropriate extensions of temporal logics. To the best of our
knowledge such attempts only covered structured languages, i.e. languages whose
structure is immediately "visible" in their sentences, such as tree-languages
or visibly pushdown ones. In this paper we present a new temporal logic
suitable to express and automatically verify properties of operator precedence
languages. This "historical" language family has been recently proved to enjoy
fundamental algebraic and logic properties that make it suitable for model
checking applications yet breaking the barrier of visible-structure languages
(in fact the original motivation of its inventor Floyd was just to support
efficient parsing, i.e. building the "hidden syntax tree" of language
sentences). We prove that our logic is at least as expressive as analogous
logics defined for visible pushdown languages yet covering a much more powerful
family; we design a procedure that, given a formula in our logic builds an
automaton recognizing the sentences satisfying the formula, whose size is at
most exponential in the length of the formula.
