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  1. Correspondence and canonicity theory of quasi-inequalities and Π2-statements in modal subordination algebras.Zhiguang Zhao - forthcoming - Logic Journal of the IGPL.
    In the present paper, we study the correspondence and canonicity theory of modal subordination algebras and their dual Stone space with two relations, generalizing correspondence results for subordination algebras in [13–15, 25]. Due to the fact that the language of modal subordination algebras involves a binary subordination relation, we will find it convenient to use the so-called quasi-inequalities and |$\varPi _{2}$|-statements. We use an algorithm to transform (restricted) inductive quasi-inequalities and (restricted) inductive |$\varPi _{2}$|-statements to equivalent first-order correspondents on the (...)
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  • Contact semilattices.Paolo Lipparini - forthcoming - Logic Journal of the IGPL.
    We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.
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