A Class of Generalised Quantifiers for k-Variable Logics
Logic
2026-02-03 v1
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.
Cite
@article{arxiv.2602.01216,
title = {A Class of Generalised Quantifiers for k-Variable Logics},
author = {Janek Härtter and Martin Otto},
journal= {arXiv preprint arXiv:2602.01216},
year = {2026}
}