Regular bilattices
Alexej P. Pynko · Journal of Applied Non-Classical Logics · 2000
A bilattice is said to be regular provided its truth conjunction and disjunction are monotonic with respect to its knowledge ordering. The principal result of this paper is that the following properties of a bilattice B are equivalent: 1. B is regular;2. the truth conjunction and disjunction of B are definable through the rest of the operations and constants of B;3. B is isomorphic to a bilattice of the form L 1 · L 2 where L 1 and L 2 are bounded lattices. We also derive from this metaequivalence a number of corollaries concerning distributive bilattices, degenerated bilattices and bilattices with negation.