On the expressive power of inquisitive team logic and inquisitive first-order logic

TL;DR

It is shown that if inquisitive team logic is extended with the range-generating universal quantifier adopted in dependence logic, the resulting logic can express finiteness, and as a consequence, it is neither compact nor recursively axiomatizable.

Abstract

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, and as a consequence, it is neither compact nor recursively axiomatizable. 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.

Theorems & Definitions (22)

• Definition 2.1
• Proposition 2.2: Persistency
• Proposition 2.3: Empty team property
• Proposition 2.4: Locality
• Definition 2.5
• Proposition 2.6
• Theorem 3.1
• proof
• Corollary 3.2
• Definition 3.3