  This paper focuses on natural dualities for varieties of bilattice-based
algebras.Such varieties have been widely studied as semantic models in
situations where information is incomplete or inconsistent. The most popular
tool for studying bilattices-based algebras is product representation. The
authors recently set up a widely applicable algebraic framework which enabled
product representations over a base variety to be derived in a uniform and
categorical manner. By combining this methodology with that of natural duality
theory, we demonstrate how to build a natural duality for any bilattice-based
variety which has a suitable product representation over a dualisable base
variety. This procedure allows us systematically to present economical natural
dualities for many bilattice-based varieties, for most of which no dual
representation has previously been given. Among our results we highlight that
for bilattices with a generalised conflation operation (not assumed to be an
involution or commute with negation). Here both the associated product
representation and the duality are new. Finally we outline analogous procedures
for pre-bilattice-based algebras (so negation is absent).
