Instructional design theories are design theories that offer explicit guidance on how to help people to learn in specific situation. They can be used to guide the design of learning activities and the arrangement of associated resources. These theories are currently expressed in natural language, but they are often given some structure in terms of methods and conditions. Tools supporting theory-based instructional design require formal models of these theories to be expressed in languages with computational semantics, thus allowing their processing. Recent research has resulted in ontologies describing theory-neutral learning activity sequences and resources in accordance with proposed standards like IMS LD, but these are not sufficient for building instructional design aid tools. This paper describes the use of formal ontologies to partially represent instructional design methods in a form that can be used to build such supporting tools. Combining ontologies describing learning activities in a learning design with rules and constraints, it is possible to encode some forms of instructional design. This paper describes such an approach using OWL and SWRL. The approach has been evaluated by building a catalogue of instructional design methods expressed in these languages, obtained from a systematic extraction from a catalogue of instructional design theories. The practical utility of the ontological schema is demonstrated by means of a relevant case study.