On the expressive power of inquisitive team logic and inquisitive first-order logic
2026-03-09 • Logic in Computer Science
Logic in Computer Science
AI summaryⓘ
The authors study inquisitive team logic, a kind of logic used to talk about questions and dependencies. They show that while sentences in this logic are as expressive as regular first-order logic, the formulas with free variables can express more complex ideas than first-order logic can. They also find that adding a special quantifier lets the logic express the concept of 'finiteness,' which makes it lose some nice technical properties like compactness and axiomatizability. Finally, they extend these findings to a broader version of inquisitive logic.
Inquisitive logicTeam semanticsFirst-order logicDependence logicUniversal quantifierExpressive powerCompactnessAxiomatizabilityFinitenessOpen formulas
Authors
Juha Kontinen, Ivano Ciardelli
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.