A pseudo-Boolean function (pBf) is a mapping from {0,1}^n to the real numbers. It is known that pseudo-Boolean functions have polynomial representations, and it was recently shown that they also have disjunctive normal forms (DNFs). In this paper we relate the DNF syntax of the classes of monotone, quadratic and Horn pBfs to their characteristic inequalities. 1 C.S.Calude and G.Stefanescu (eds.). Automata, Logic, and Computability. Special issue dedicated to Professor Sergiu Rudeanu Festschrift.