The Distributed Ontology Language DOL, which is currently being standardised as ISO WD 17347 within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3, aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies.

A DOL ontology consists of modules formalised in basic ontology languages, such as OWL or Common Logic, which are serialised in the existing syntaxes of these languages. On top of this, DOL provides a meta-level which allows for expressing heterogeneous ontologies and links between ontologies. Such links include (heterogeneous) imports and alignments, conservative extensions, and theory interpretations. This paper focuses on the abstract syntax and semantics of these meta-level constructs. It introduces three alternative semantics for the meta-level, namely direct, translational, and collapsed semantics (the latter is only briefly sketched), and studies their respective pros and cons.