A Discrete Representation of Lattice Frames.
LORI(2019)
摘要
We characterize those doubly ordered frames
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that are embeddable into the canonical frames of their complex algebras defined by Alasdair Urquhart in his representation theorem for bounded general lattices [ 31 ]. Our result together with the topology-free version of Urquhart’s representation leads to a discrete (i.e. topology free) duality for bounded general lattices. We also show that doubly ordered frames are definable neither in a logic endowed with only a possibility operator nor a logic with only a sufficiency operator, but in a logic based on mixed algebras with both a possibility and a sufficiency operator.
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