## 3 DL-Based Ontology
### Top-Level Entities  
LPBF is an AM process whose energy source is a laser beam, build material is a powder material, build platform is a powder bed, and build mechanism is melting. Process planning for LPBF is a product realisation activity that aims to design appropriate process variables to build a part that can satisfy certain build and quality requirements. The main inputs of this activity include a 3D model, an LPBF material, an LPBF machine, and build and quality requirements. The outputs of the activity are a set of process variables, which include build orientation, support structure, slices, laser scanning path, and process parameters. Figure 2: Schematic diagram of the development process of the DL-based ontology. Process planning consists of four successive tasks that of part orientation, that of support generation, that of model slicing, and that of path planning [55]. Based on the description above, twenty-eight top-level concepts were created and depicted in Figure 3. Among them, _Lpbf_, _Lpbf_Part_, _Lpbf_Material_, _Lpbf_Machine_, _ProcessPlanning_, _PartOrientation_, _SupportGeneration_, _ModelSlicing_, and _PathPlanning_ are composite concepts (concepts that need to be defined by other concepts), while the remaining concepts are atomic concepts (concepts that cannot be defined by other concepts). The DL definitions of the nine composite concepts are given by the following terminological axioms:  
\[Lpbf\equiv AmProcess\sqcap\exists hasEnergySource.LaserBeam\sqcap\exists hasBuildMaterial. PowderMaterial \tag{1}\] \[\sqcap\exists hasBuildPlatform.PovderBed\sqcap\exists hasBuildMechanism.Melting\] (2) \[LpbfPart\equiv AmPart\sqcap\exists isManufacturedUsing.Lpbf\] (3) \[LpbfMaterial\equiv PowderMaterial\sqcap\exists isApplicableFor.Lpbf\] (4) \[LpbfMachine\equiv AmMachine\sqcap\exists isBasedOn.Lpbf\] (5) \[ProcessPlanning\equiv RealisationActivity\sqcap\exists has AimOfDesigning.ProcessVariable\] (6) \[PartOrientation\equiv ProcessPlanning\sqcap\exists has AimOfDesigning.BuildOrientation\] (7) \[SupportGeneration\equiv ProcessPlanning\sqcap\exists has AimOfDesigning.SupportStructure\] (8) Figure 3.0  
Figure 3.1 Graphical representation of top-level concepts and their hierarchies. \[ \begin{array}{lcl}\mathit{PathPlanning}\equiv\mathit{ProcessPlanning}&\sqcap&\exists\mathit{hasAimOfDesigning.LaserScanningPath}\\ &\sqcap&\exists\mathit{hasAimOfDesigning.ProcessParameter}\end{array}  \tag{9}\]  
where \(\equiv\) is the concept definition symbol in DLs which is used to define a concept, \(\exists\) is the existential restriction symbol in DLs which is used to denote that there are one or more instances of a concept that have a specific relation, \(\sqcap\) is the concept conjunction symbol in DLs which is used to obtain the intersection of instances of two concepts, and \(\mathit{hasEnergySource}\), \(\mathit{hasBuildMaterial}\), \(\mathit{hasBuildPlatform}\), \(\mathit{hasBuildMechanism}\), \(\mathit{hasAimOfDesigning}\), \(\mathit{isManufacturedUsing}\), \(\mathit{isApplicableFor}\), and \(\mathit{isBasedOn}\) are object relations whose domain, range, and meaning are listed in Table 3.  
The build and quality requirements are specified by process planners based on certain indicators. Indicators for describing the build requirements of an LPBF part mainly include support volume, build time, and build cost, while indicators for specifying the quality requirements of an LPBF part mainly contain dimensional error, geometric error, volumetric error, surface roughness, density, hardness, yield strength, tensile strength, elongation, residual stress, and fatigue strength. In the process of planning for LPBF, the values of these indicators for an LPBF part to be built are usually predicted via certain prediction models.