latticewith
Latticewith is a term used in some mathematical and computer science contexts to denote a lattice that is equipped with an additional binary operation, commonly referred to as “with.” The idea behind latticewith is to study how an operation that combines two lattice elements interacts with the underlying order and lattice operations, such as join and meet. The term is not universally standardized and may be defined differently across sources, but the central notion is a lattice augmented by a second, well-behaved operation.
Formally, a latticewith consists of a lattice (L, ≤, ∨, ∧) together with a binary operation with: L ×
Examples often cited include taking the power set lattice with union as the join and with as
See also: lattice, semilattice, formal concept analysis, lattice-ordered structures, data fusion.