Engineering is often said to be ‘scientific’, but the nature of knowledge in engineering is different to science. Engineering has a different ontological basis—its theories address different entities and are judged by different criteria. In this paper I use Popper’s three worlds ontological framework to propose a model of engineering theories, and provide an abstract logical view of engineering theories analogous to the deductive-nomological view of scientific theories. These models frame three key elements from definitions of engineering: requirements, designs of artefacts, and theories for reasoning about how artefacts will meet requirements. In a subsequent paper I use this ontological basis to explore methodological issues in the growth of engineering knowledge from the perspective of critical rationalism.