## 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.

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#### 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.

#### BibTeX: (download)

@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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