Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Information flow: the logic of distributed systems
Information flow: the logic of distributed systems
Multi lingual sequent calculus and coherent spaces
Fundamenta Informaticae
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
ICCS'05 Proceedings of the 13th international conference on Conceptual Structures: common Semantics for Sharing Knowledge
ICFCA'07 Proceedings of the 5th international conference on Formal concept analysis
ICFCA'11 Proceedings of the 9th international conference on Formal concept analysis
On links between concept lattices and related complexity problems
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
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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.