Abstract
Formal Concept Analysis
Galois connections between concept lattices can be represented as binary
relations on the context level, known as dual bonds. The latter also appear as
the elements of the tensor product of concept lattices, but it is known that not all
dual bonds between two lattices can be represented in this way. In this work, we
define regular Galois connections as those that are represented by a dual bond in
a tensor product, and characterize them in terms of lattice theory. Regular Galois
connections turn out to be much more common than irregular ones, and we identify
many cases in which no irregular ones can be found at all. To this end, we
demonstrate that irregularity of Galois connections on sublattices can be lifted to
superlattices, and observe close relationships to various notions of distributivity.
This is achieved by combining methods from algebraic order theory and FCA
with recent results on dual bonds. Disjunctions in formal contexts play a prominent
role in the proofs and add a logical flavor to our considerations. Hence it
is not surprising that our studies allow us to derive corollaries on the contextual
representation of deductive systems.
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