Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce the concepts of abstract inference modules and abstract modular inference systems to study general principles behind the design and analysis of model-generating programs, or solvers, for integrated multilogic systems.We show how modules and modular systems give rise to transition graphs, which are a natural and convenient representation of solvers, an idea pioneered by the SAT community. We illustrate our approach by showing how it applies to answer-set programming and propositional logic, and to multi-logic systems based on these two formalisms.