Two - Variable Logic on Data

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. This model has been already considered in the realm of semistructured data, timed automata and extended temporal logics. This paper shows that satisfiability for the two-variable fragment FO(∼,<,+1) of firstorder logic with data equality test ∼, is decidable over finite and over infinite data words. Here, +1 and < are the usual successor and order predicates, respectively. The satisfiability problem is shown to be at least as hard as reachability in Petri nets. Several extensions of the logic are considered, some remain decidable while some are undecidable.