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In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form $${\forall x_0 \exists x_1 \dots \exists x_n \bigwedge x_i R_\lambda x_j}$$ ∀ x 0 ∃ x 1 ⋯ ∃ x n ⋀ x i R λ x j . We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a...
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