  We propose FC, a new logic on words that combines finite model theory with
the theory of concatenation - a first-order logic that is based on word
equations. Like the theory of concatenation, FC is built around word equations;
in contrast to it, its semantics are defined to only allow finite models, by
limiting the universe to a word and all its factors. As a consequence of this,
FC has many of the desirable properties of FO on finite models, while being far
more expressive than FO[<]. Most noteworthy among these desirable properties
are sufficient criteria for efficient model checking, and capturing various
complexity classes by adding operators for transitive closures or fixed points.
  Not only does FC allow us to obtain new insights and techniques for
expressive power and efficient evaluation of document spanners, but it also
provides a general framework for logic on words that also has potential
applications in other areas.
