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A Model Theory of Topology

Studia Logica:1-35 (forthcoming)

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  1. Contact semilattices.Paolo Lipparini - 2024 - Logic Journal of the IGPL 32 (5):815-826.
    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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  • Hypercontact semilattices.Paolo Lipparini - forthcoming - Journal of Applied Non-Classical Logics:1-26.
    Boolean algebras are one of the main algebraic tools in the region-based theory of space. T. Ivanova provided strong motivations for the study of mere semilattices with a contact relation. Another significant motivation for considering an even weaker underlying structure comes from event structures with binary conflict in the theory of concurrent systems in computer science. All the above-hinted notions deal with a binary contact relation. Several authors suggested the more general study of n-ary ‘hypercontact’ relations. A similar evolution occurred (...)
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