An equational theory for trilattices (Q5950770)

The triadic approach to Formal Concept Analysis was introduced by R. Wille in 1995. It gives rise to so-called trilattices which are sets with three orders satisfying the so-called uniqueness condition and antiordinal dependency where certain operations, so-called ik-joins, exists. Algebraically, they are characterized by nine types of trilattice equations. The Reduction Theorem guarantees that if ik-joins of arity \((2,2)\) exist then all finitary ik-joins exist. An axiomatization of these operations is included in Theorems 3.1 and 4.1.