Ontologies are widely used for achieving interoperable Digital Twins (DTws), yet competing DTw definitions compound interoperability issues. Semantically linking these differing twins is feasible through ontologies and Cognitive Digital Twins (CDTws). However, it is often unclear how ontology use bolsters broader DTw advancements. This article presents a systematic survey following the PRISMA method, to explore the potential of ontologies to support DTws to meet the Centre for Digital Built Britain's Gemini Principles and aims to link progress in ontologies to this framework. The Gemini Principles focus on common DTw requirements, considering: Purpose for 1) Public Good, 2) Value Creation, and 3) Insight; Trustworthiness with sufficient 4) Security, 5) Openness, and 6) Quality; and appropriate Functionality of 7) Federation, 8) Curation, and 9) Evolution. This systematic literature review examines the role of ontologies in facilitating each principle. Existing research uses ontologies to solve DTw challenges within these principles, particularly by connecting DTws, optimising decisionmaking, and reasoning governance policies. Furthermore, analysing the sectoral distribution of literature found that research encompassing the crossover of ontologies, DTws and the Gemini Principles is emerging, and that most innovation is predominantly within manufacturing and built environment sectors. Critical gaps for researchers, industry practitioners, and policymakers are subsequently identified.