On the Expressive Power of Inquisitive Team Logic and Inquisitive First-Order Logic
For logicians and philosophers interested in the foundations of dependence and inquisitive semantics, this work clarifies the expressive boundaries of these logics, revealing unexpected strength.
The paper shows that inquisitive team logic and inquisitive first-order logic have expressive power beyond first-order logic for open formulas, and that some sentences of inquisitive first-order logic express non-first-order properties, solving an open problem.
Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be expressively equivalent with first-order logic. In this article we show that, on the contrary, the expressive power of open formulas in this logic properly exceeds that of first-order logic. On the way to this result, we show that if inquisitive team logic is extended with the range-generating universal quantifier adopted in dependence logic, the resulting logic can express finiteness; as a consequence, this logic is not compact and has non-arithmetic complexity. We further extend our results to standard inquisitive first-order logic, showing that some sentences of this logic express non first-order properties of models, thus settling an open problem from the literature.