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

2026-03-09

AI Summary

This study investigates whether open formulas in interrogative team logic possess expressive power beyond that of classical first-order logic. By employing team semantics and model-theoretic techniques, and extending the analysis with universal quantification from dependence logic, the paper provides the first rigorous proof that open formulas in interrogative team logic indeed exhibit super-first-order expressivity. The extended system can define non-first-order properties such as finiteness, which consequently leads to failure of compactness and the impossibility of recursive axiomatization. This work establishes the capacity of interrogative first-order logic to express inherently non-first-order properties at the model-theoretic level, thereby revealing a fundamental boundary separating it from classical logic.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• inquisitive team logic
• inquisitive first-order logic
• expressive power
• first-order logic
• finiteness

Innovation

• inquisitive team logic
• expressive power
• open formulas
• finiteness
• non-first-order properties