# Simulations and Bisimulations For Coalgebraic Modal Logics

arXiv: https://arxiv.org/abs/1303.2467 · HTML: https://mlsanity.com/paper/1303.2467/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2013.

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

- [Coalgebraic Fuzzy geometric logic](https://mlsanity.com/paper/2205.13387/) (2022)

## Abstract (arXiv)

We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii) for Lambda a separating set of monotone predicate liftings, the associated notion of Lambda-bisimulation corresponds to T-behavioural equivalence (moreover Lambda-n-bisimulations correspond to T-n-behavioural equivalence), and iii) in fact, for Lambda-separating and T preserving weak pullbacks, difunctional Lambda-bisimulations are T-bisimulations. In essence, we arrive at a modular notion of equivalence that, when used with a separating set of monotone predicate liftings, coincides with T-behavioural equivalence regardless of whether T preserves weak pullbacks (unlike the notion of T-bisimilarity).