Computational form-finding methods hold great potential concerning resource-efficient structural design. The Combinatorial Equilibrium Modeling (CEM), an equilibrium-based form-finding method based on graphic statics and graph theory, allows the design of cross-typological tension–compression structures starting from an input topology diagram in the form of a graph. This paper presents a novel Logic-Informed Graph Neural Network (LIGNN) that integrates the validity conditions of CEM topology diagrams into the learning process through semantic loss terms. A Primary-LIGNN (P-LIGNN) and a Modification-LIGNN (M-LIGNN) are introduced and incorporated together with the CEM into a general form-finding-based computational structural design workflow that transforms input topologies into parametric models of equilibrium structures. An implementation of this computational design workflow for the conceptual design of pedestrian bridge structures is made, and presented through a case study, for which a synthetic training dataset of topology diagrams for the LIGNNs has been developed.