1 research outputs found
The Lattice of Congruences of a Finite Line Frame
Let be a finite Kripke frame. A
congruence of is a bisimulation of that is also an
equivalence relation on F. The set of all congruences of is a
lattice under the inclusion ordering. In this article we investigate this
lattice in the case that 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
, the interval embeds into the lattice of
divisors of a suitable positive integer. We also prove that any two congruences
with a nontrivial upper bound permute.Comment: 31 pages, 11 figures. Expanded intro, conclusions rewritten. New,
less geometrical, proofs of Lemma 19 and (former) Lemma 3