# Modal Characterisations of Behavioural Pseudometrics

arXiv: https://arxiv.org/abs/1509.03391 · HTML: https://mlsanity.com/paper/1509.03391/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2015.

## Built on by (most cited first, 1 of 1)

- [A Foundational Theory of Quantitative Abstraction: Adjunctions, Duality, and Logic for Probabilistic Systems](https://mlsanity.com/paper/2510.19444/) (2025)

## Abstract (arXiv)

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on the Hennessy-Milner logic. The logic for characterising the state-based metric is much simpler than an earlier logic by Desharnais et al. as it uses only two non-expansive operators rather than the general class of non-expansive operators.