A Formal Definition of Object-Action Complexes and Examples at Different Levels of the Processing Hierarchy Norbert Kr¨ uger, Justus Piater, Florentin W¨org¨otter, Christopher Geib, Ron Petrick, Mark Steedman, Aleˇ s Ude, Tamim Asfour, Dirk Kraft, Damir Omrˇ cen, Bernhard Hommel, Alejandro Agostini, Danica Kragic, Jan-Olof Eklundh, Volker Kr¨ uger, Carme Torras, and R¨ udiger Dillmann April 20, 2009 1 Introduction The purpose of this paper is to give a coherent definition and notation for Object–Action Complexes (in the following called ’OACs’) within the PACO-PLUS consortium. To further clarify the OAC concept we provide — besides the formal definition — a number of examples of OACs at differ- ent levels of the processing hierarchy and also some examples of the use of OACs for the formalization of behaviours of different degrees of complexity. The work here is to be seen as a summary of a converging discussion pro- cess about OACs within the PACO-PLUS consortium. Of course, a difficult topic such as the OAC concept is still open for modifications. This deliv- erable is meant to provide a formal definition to be used as a basis for the implementation of OACs to further guide the discussion process. This work is based on some prior publications on OACs (see [7, 21]). In section 2 we give a motivation for object-action complexes. Section 3 continues with the formal definition of OACs, while in Section 4 a number of examples at different levels of the processing hierarchy are described. In section 5 we discuss some outstanding issues related to OACs, which need to be considered in our future work. 1