Halldén complete modal logics are defined semantically. They have a nice characterization as they are determined by homogeneous Kripke frames.

We consider the family of logics from NExt which are determined by linear frames with reflexive and symmetric relation of accessibility. The condition of linearity in such frames was first defined in the paper [9]. We prove that the cardinality of the logics under consideration is uncountably infinite.

We define a special family of Brouwerian logics determined by linearly ordered frames. Then we prove that all logics of this family have the finite model property and are Kripke complete.