An Ehrenfeucht-Fraïssé Game for Inquisitive First-Order Logic
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Abstract
Inquisitive first-order logic, InqBQ, is an extension of classical first-order logic with questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. In this paper we describe an Ehrenfeucht-Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. We exploit this result to show a number of undefinability results: in particular, several variants of the question how many individuals have property P are not expressible in InqBQ, even in restriction to finite models.
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