In highly networked systems, such as Industry 4.0, it is essential to take care that only trustworthy elements participate in the network, otherwise the security of the system might be compromised and its functionality negatively influenced. Therefore it is important to identify whether the nodes in the network can be trusted by other elements of the system. The Industry 4.0 involves both human and artificial participants and imposes human-human, artefact-artifact; and human-artefact relationships in the system. This requires comparable interpretation and representation of trust in several areas. For this purpose the paper discusses three trust interpretations (in social sciences, in information systems, and distributed ad-hoc networks) and respective multidimensional trust models; and shows how the elements of the of these trust models can be integrated in the trust handling framework for in Industry 4.0.