Back and Forth Between First-Order Kripke Models

Połacik, Tomasz

doi:10.1093/jigpal/jzn011

Cited by 4 publications

(1 citation statement)

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“…The basic idea of EF games has proven to be very flexible and adaptable to a wide range of logical settings, including fragments of first-order logic with finitely many variables [14]; extensions of first-order logic with generalized quantifiers [15]; monadic second order logic [8]; modal logic [24]; and intuitionistic logic [18,25]. In each case, the game provides an insightful characterization of the distinctions that can and cannot be made by means of formulas in the logic.…”

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confidence: 99%

Games and Cardinalities in Inquisitive First-Order Logic

Grilletti¹,

Ciardelli²

2021

The Review of Symbolic Logic

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Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what statements and questions can be expressed in InqBQ about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question how many individuals satisfy $\alpha (x)$ are not expressible in InqBQ, both in the general case and in restriction to finite models.

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confidence: 99%