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The collection of all subject-object pairs sharing a predicate, together with their epistemic values. The basic unit of the fiber functor.

A predicate fiber is the collection of all subject-predicate-object triples sharing a given predicate, together with their values.

For a predicate pp in a system of SPO triples S\mathcal{S}:

Fib(p)={s,o,v:s,p,oS with value v}\mathrm{Fib}(p) = \{ \langle s, o, v \rangle : \langle s, p, o \rangle \in \mathcal{S} \text{ with value } v \}

When values are drawn from the four-valued bilattice, the fiber inherits bilattice algebra pointwise: the operations \odot (extending) and \Rightarrow (restricting) from the Busaniche-Cignoli residuation apply to each entry in the fiber.

The assignment pFib(p)p \mapsto \mathrm{Fib}(p) 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.

Last reviewed .

Relations

Adjunction on fiber
⊙ ⊣ ⇒
Date created
Defines
predicate fiber
Functor assignment
p ↦ A p
Functor is
contravariant
Functor target
distributive bilattice
In fca terms
column of a formal context
In feature structure terms
all entities' values for a single attribute
Indexed by
predicate
Introduces
fiber
Pattern
hyperdoctrine
Pointwise operations
  • truth meet
  • truth join
  • knowledge meet
  • knowledge join
Values in
epistemic state