Normal Modal Logics Determined by Aligned Clusters

Abstract

Abstract.We consider the family of logics from NExt(KTB) 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.

On Halldén Completeness of Modal Logics Determined by Homogeneous Kripke Frames

“…We Remark 2. The cardinality of the whole family N EXT (KTB.alt 4 ) is that of the continuum (see [9]). We have defined an anti-chain of Halldén complete logics in N EXT (KTB.alt 4 ) and it seems to be possible to define a continuum of logics by taking their infinite intersections.…”

Interpolation in Normal Extensions of the Brouwer Logic

“…In contrast to N EXT (KTB.Alt(3)), the family of logics N EXT (KTB.Alt(4)) := KTB ⊕ alt 4 is uncountably infinite, see [10].…”