Scott and Engeler proposed almost fifty years ago Arrow Terms of the form {a1, a2,…, an} → b as a model for combinatory logic. Arrow terms describe directed graphs, such as neural networks. Thus, it is called the Graph Model of Combinatory Logic. Combinatory logic is Turing-complete, thus there exists a model for knowledge that includes both theoretical computer science and engineering of Artificial Intelligence (AI). The graph model provides an accurate theoretical definition for knowledge, but in practice its arrow terms reflect the structure of nodes in a large artificial neural network. Knowledge relies on observations, ignoring cause and effect, or any sort of theory outside statistical evidence. A theory is knowledge under control that can be approximated by control sequences. Theories can be formulated in the graph model as well, but theories avoid hallucinations. The combination of knowledge and theories enables Intelligent Systems, systems that continuously learn and adapt, incorporating both AI engines and traditional programs. The graph model explains how AI works, how to avoid hallucinations, and prepares AI-based applications for safety certificates, based on an intuitionistic mathematical approach.