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arXiv · 2602.01216

A Class of Generalised Quantifiers for k-Variable Logics

Janek Härtter·Martin Otto
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Abstract

We introduce k-quantifier logics -- logics with access to k-tuples of elements and very general quantification patterns for transitions between k-tuples. The framework is very expressive and encompasses e.g. the k-variable fragments of first-order logic, modal logic, and monotone neighbourhood semantics. We introduce a corresponding notion of bisimulation and prove variants of the classical Ehrenfeucht-Fraisse and Hennessy-Milner theorem. Finally, we show a Lindstrom-style characterisation for k-quantifier logics that satisfy Los' theorem by proving that they are the unique maximally expressive logics that satisfy Los' theorem and are invariant under the associated bisimulation relations.

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Janek Härtter, Martin Otto. 2026-02-01. A Class of Generalised Quantifiers for k-Variable Logics. https://arxiv.org/abs/2602.01216

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