International audienceIn a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO2(~, <, +1) is decidable over finite and over infinite data words, where ~ is a binary predicate testing the data value equality and +1,< are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable

Motivated by reasoning tasks in the context of XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result decidability of satisfiability and containment for a dataaware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.

Abstract. We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we generalize nominal sets due to Gabbay and Pitts.

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 article shows that satisfiability for the two-variable fragment FO 2 (∼,<,+1) of first-order logic with data equality test ∼ is decidable over finite and 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.

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