## The Lattice of Congruences of a Finite Line Frame

C. Areces, M. Campercholi, D. Penazzi, and P. Sánchez Terraf. The Lattice of Congruences of a Finite Line Frame. Journal of Logic and Computation, 2017.

#### Abstract:

Let F = <F, R> be a finite Kripke frame. A congruence of F is a bisimulation of F that is also an equivalence relation on F. The set of all congruences of F is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that F is a finite line frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through these descriptions we show that for every nontrivial congruence \rho, the interval [Id_F, \rho] embeds into the lattice of divisors of a suitable positive integer. We also prove that any two congruences with a nontrivial upper bound permute.

@ARTICLE{arec:latti17,
author = {C. Areces and M. Campercholi and D. Penazzi and P. Sánchez Terraf},
title = {The Lattice of Congruences of a Finite Line Frame},
journal = {Journal of Logic and Computation},
year = {2017},
abstract = {Let F = <F, R> be a finite Kripke frame. A congruence of F is a bisimulation
of F that is also an equivalence relation on F. The set of all congruences
of F is a lattice under the inclusion ordering. In this article we
investigate this lattice in the case that F is a finite line frame.
We give concrete descriptions of the join and meet of two congruences
with a nontrivial upper bound. Through these descriptions we show
that for every nontrivial congruence \rho, the interval [Id_F, \rho]
embeds into the lattice of divisors of a suitable positive integer.
We also prove that any two congruences with a nontrivial upper bound
permute.},
owner = {areces},
timestamp = {2017.12.04}
}


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