A predicate fiber is the collection of all subject-predicate-object triples sharing a given predicate, together with their values.
For a predicate in a system of SPO triples :
When values are drawn from the four-valued bilattice, the fiber inherits bilattice algebra pointwise: the operations (extending) and (restricting) from the Busaniche-Cignoli residuation apply to each entry in the fiber.
The assignment is a functor — the fiber functor — from the category of predicates to distributive bilattices. This makes any SPO system a hyperdoctrine with bilattice fibers.
In formal concept analysis terms, a predicate fiber is the column of a formal context: all objects’ values for a single attribute. In typed feature structure terms, it is all entities’ values for a single feature.
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