Abstract. In this paper we thoroughly investigate several kinds of residuated ordered structures, connected with propositional logics. In particular we give ternary deduction terms for several classes of algebras, that are the equivalent algebraic semantics of deductive systems, coming from logics not necessarily satisfying the structural rules.

AMS Subject Classification (1991): 08A99, 06F05

Received December 27, 1996, in revised form April 20, 1998 and in final form May 18, 1998. (Registered under 3296/2009.)