  Bi-Intuitionistic Stable Tense Logics (BIST Logics) are tense logics with a
Kripke semantics where worlds in a frame are equipped with a pre-order as well
as with an accessibility relation which is 'stable' with respect to this
pre-order. BIST logics are extensions of a logic, BiSKt, which arose in the
semantic context of hypergraphs, since a special case of the pre-order can
represent the incidence structure of a hypergraph. In this paper we provide,
for the first time, a Hilbert-style axiomatisation of BISKt and prove the
strong completeness of BiSKt. We go on to prove strong completeness of a class
of BIST logics obtained by extending BiSKt by formulas of a certain form.
Moreover we show that the finite model property and the decidability hold for a
class of BIST logics.
