Team Semantics and Recursive Enumerability

It is well known that dependence logic captures the complexity class NP, and it has recently been shown that inclusion logic captures P on ordered models. These results demonstrate that team semantics offers interesting new possibilities for descriptive complexity theory. In order to properly understand the connection between team semantics and descriptive complexity, we introduce an extension D∗ of dependence logic that can define exactly all recursively enumerable classes of finite models. Thus D∗ provides an approach to computation alterative to Turing machines. The essential novel feature in D∗ is an operator that can extend the domain of the considered model by a finite number of