In an effort to continue the pioneering work of Harary in USA and Flament in France, we have undertaken to develop, on an experimental basis, a formalized theory of systems of beliefs and their modifications. This theory uses the psycho-social concepts of theories of cognitive consistency and of the tools of discrete mathematics, such as rewriting and intervals within graphs. The axioms and rewriting rules are elaborated from experimental data, and we demonstrate that the system we have built has the property of termination. This result is in accordance with experimental observations that show that every subject having an inconsistent system of beliefs (i.e., one containing contradictions) makes this system evolve towards consistency to reach a simple, consistent reference framework.