# Reasoning About Bounds in Weighted Transition Systems

arXiv: https://arxiv.org/abs/1703.03346 · HTML: https://mlsanity.com/paper/1703.03346/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2017.

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

- [Epistemic Skills: Reasoning about Knowledge and Oblivion](https://mlsanity.com/paper/2504.01733/) (2025)

## Abstract (arXiv)

We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates states that exhibit transitions to bisimulation classes with the weights within the same boundaries. We propose a customized modal logic that expresses these numeric boundaries for transition weights by means of particular modalities. We prove that our logic is invariant under the proposed notion of bisimulation. We show that the logic enjoys the finite model property and we identify a complete axiomatization for the logic. Last but not least, we use a tableau method to show that the satisfiability problem for the logic is decidable.