  This paper fills a gap in the literature on natural duality theory. It
concerns dual representations of categories of distributive-lattice-based
algebras in which the lattice reducts are not assumed to have bounds. The
development of theory to parallel what is known for the exhaustively-studied
bounded case was initially driven by need. This arose in connection with a
major investigation of Sugihara algebras and Sugihara monoids. The theorems in
this paper apply in a systematic way to a range of examples:varieties of
Sugihara type; other classes of algebras previously treated ad hoc; and further
classes as required.
