## 3 Printing Information Model for Additive Manufacturing of Concrete Structures
### Formal Modeling of the Printing Information  
Unified Modeling Language, allowing for the visualization of semantics in great detail and being easily comprehensible for engineers, supports the development of software tools and information systems necessary for designing and planning concrete printing projects. However, UML is bound to closed-world assumptions and may contain design errors leading to unsatisfiable concepts [38]. To enable open-world assumptions for knowledge based reasoning, to provide vocabulary, and to verify the PIM model's satisfiability, a printing information ontology that formalizes the previous UML class diagram for the Web Ontology Language (OWL) is developed. Based on the ontology, the PIM model is refined in an iterative process. The ISO-standardized Basic Formal Ontology (BFO) is used as an upper-level ontology as it provides support for information exchange [39]. Classes referring to objects and materials are aligned with the top-level entity _BFO:Material_entity_, classes referring to geometry representations and sites are aligned with the top-level entity _BFO:Immaterial_entity_, classes referring to quality information are aligned with the _BFO:Quality_ entity, and classes referring to processes are aligned with the _BFO:Occurrent_ entity. Attributes of the classes are defined as data properties, while multiplicity conditions are described with cardinality axioms. Furthermore, the semantic relationships between the classes are described using class properties, axioms, and description logic (DL) rules. Figure 5 shows an extract of the alignment of the classes with the BFO hierarchy for the printing information ontology, hereinafter referred to as PIM-O. The PIM-O is built following a bottom-up construction strategy, allowing alignment with other domain ontologies, such as ifcOWL [40]. For example, concepts in ifcOWL have been enhanced using BFO as a basis to improve interoperability [41]. Figures 6 and 7 present extracts of the PIM-O to illustrate the class hierarchy and semantic relationships. An overview of axioms in PIM-O is provided in Appendix B. The class hierarchy has been defined in compliance with the BFO upper-level ontology and the ifcOWL domain ontology with eight top-level classes: _Geometry_, _Function_, _Material_, _Object_, _Process_, _Quality_, _Role_, and _Site_. The ontology can be represented in four views: (i) component view, (ii) process view, (iii) material view, and (iii) geometry view. In the component view (Figure 6a), all views are linked and contextualized within concrete printing projects, where an _AMComponent_, representing building elements (e.g., walls, columns, beams, and support structures), is part of a _Building_ and has qualities such as structural properties (_Structural_property_) and load patterns (_Load_pattern_). Furthermore, a _Component_ is an output of an _AMPProcess_, which has materials (_Material_) as a resource and takes digital models (_Geometry_) as inputs. As can be noted, the ontology further formalizes the semantic relationships described in the UML-based printing information model. In a similar manner, the process, material, and geometry views are defined, where relevant semantic relationships are described below. Figure 5: Extract of the alignment of classes according to the BFO hierarchy for the printing information ontology (PIM-O). In the process view (Figure 6b), AM processes are described according to the definitions and concepts stated in the international standards [1; 17; 30], focusing on extrusion-based AM methods. An _AM_process_, comprising tasks (_AM_task_), is characterized by building components in a layer-by-layer manner, using resources such as machines (_Machine_) and materials (_Material_). AM processes have actors (_Actor_) involved in the tasks with roles and functions, as defined in Section 2. Furthermore, process qualities include machine data, slicing data, toolpath data, control data, monitoring data, and process boundary conditions.