Structural multiplicity has a significant effect on the solution of an MINLP model for process synthesis problems. The optimization model may also have built-in redundancy that cannot always be directly derived from the multiplicity of the superstructure. A basic GDP representation (BGR) involving logical relations is defined, and can be constructed by applying a standard natural representation of the process. Basic MINLP representation (BMR) is defined by transforming the logical relations to algebraic ones. MINLP representation (MR) is defined through a fixed form of BMR. Equivalency and representativeness of MR-s in general form can be analyzed by reducing them to their BMRs. BMR can be automatically generated, and can serve as a reference representation. Binary and continuous multiplicity of MR are defined. If the supergraph, i.e. the graph representing the superstructure, is structurally redundant (i.e. there are isomorphic graphs amongst their subgraphs) then BMR has binary multiplicity. Conversely, the structural redundancy of the graph does not follow from the binary multiplicity of its BMR. Different kinds of multiplicity and redundancy measures of the MINLP representation will be defined in Part 11 of this series in order to help inventing tools for decreasing their detrimental effect. Alternative MINLP representations will there be defined, constructed, and compared from the viewpoint of ideality, minimality, and solution properties. (c) 2005 Elsevier Ltd. All rights reserved.