Table 1.
Definitions of the Basic Types of Material Entity of the Basic Formal Ontology (BFO Version 1.1).
Figure 1.
A constitutive granularity of molecules, cells and organs of a multicellular organism. It is characteristic of constitutive granularities that all objects belonging to one level of granularity are parts of objects of the next coarser level of granularity: all molecules are part of cells, all cells part of organs, and all organs part of multicellular organisms. Moreover, the sum of all objects of one level of a constitutive granularity yields the maximal object, which is in this case a multicellular organism.
Figure 2.
Granular Representation of a Particular Fiat Cell Part, Cell, and Cell Aggregate.
At the cellular level a particular fiat cell part instantiates the ‘fiat cell part’ category, which is a subcategory of ‘fiat object part’. A particular cell instantiates the ‘cell’ category, which is a subcategory of ‘object’. A particular cell aggregate instantiates the ‘cell aggregate’ category, which is a subcategory of ‘object aggregate’. At the finer molecular level, they all instantiate different subcategories of ‘molecule aggregate’ (i.e. subcategories of ‘object aggregate’). At the coarser organ and multicellular organism level they instantiate subcategories of ‘fiat organ part’ and ‘fiat multicellular organism part’ (i.e. subcategories of ‘fiat object part’). In some cases a particular cell aggregate instantiates a subcategory of ‘organ’ (i.e. subcategory of ‘object’). Although each particular entity instantiates multiple categories, these categories do not necessarily have to stand in a class-subclass relation to one another. Instead, they are different granular representations (see 2.2.3 Granular Representation and the Single Inheritance Principle) of the same specific type of material entity (i.e. FIAT CELL PART, CELL, CELL AGGREGATE).
Figure 3.
First Order Categories of Material Entity.
A) –C) The three different top-level categories of material entity that the Basic Formal Ontology currently distinguishes (BFO, version 1.1). D) & E) Two additional top-level categories of material entity that are currently not recognized by BFO. With the exception of ‘object’, all categories possess some fiat boundary and thus are fiat wholes. (modified from [4]).
Figure 4.
Taxonomy of Top-Level Categories of Constitutively Organized Material Entities.
A taxonomy of top-level categories of material entity and important subcategories that can be distinguished in constitutively organized material entities. Black boxes indicate Basic Formal Ontology (BFO) categories of material entity and dark grey boxes the additional categories suggested by [4]. (modified from [4]).
Table 2.
Definitions of additional Top-Level Categories of Material Entity for the Basic Formal Ontology (from [4]).
Figure 5.
Second Order Categories of Material Entity.
Possible subcategories of the three top-level categories of material entity aggregates (I–III) that can be differentiated on grounds of distinguishing two types of relation between the entities of the aggregate (i.e. metric proximity and topological adherence) and the presence or lack of fiat boundariesimmat: (i) Clusters are not demarcated by fiat boundariesimmat and are further characterized by topological adherence relations between the entities of the aggregate (through chemical bonds or physical junctions). (ii) Groups are demarcated by fiat boundariesimmat and are further characterized by metric proximity relations between the entities of the aggregate – they lack adherence. Since also several clusters can spatially relate to one another on grounds of metric proximity, clusters can be parts of groups as well. A)–D) The four subcategories of ‘object aggregate’ – an ‘object cluster’ and three subcategories of ‘object group’, all of which either consist of objects, object clusters, or both. Note that an object cluster is only demarcated by bona fide boundaries and thus does not represent a fiat whole. E)–H) The four subcategories of ‘fiat object part aggregate’ – a ‘fiat object part cluster’ and three subcategories of ‘fiat object part group’, all of which either consist of fiat object parts, fiat object part clusters, or both. I)–K) Four out of 26 subcategories of ‘object with fiat object part aggregate’ – an ‘object with fiat object part cluster’ and three out of 25 possible subcategories of ‘object with fiat object part group’. Fiat boundarymat: demarcates fiat parts of a material entity; fiat boundaryimmat: demarcates fiat parts of an immaterial entity (i.e. a hole). (modified from [4]).
Table 3.
Three Foundational Types of Spatio-Topological Relations between Material Entities (from [4]).
Figure 6.
Cumulative Constitutive Granularity.
A cumulative constitutive granularity of a multicellular organism consisting of molecules, organelles, cells, and organs. It is characteristic of cumulative constitutive granularities that not all objects belonging to one granularity level are parts of objects at the next coarser level of granularity – they only have to be part of the maximal whole, which is in this case a multicellular organism. Molecules exist that are not part of cells and cells that are not part of organs. As a consequence, the sum of all objects of one level of a cumulative constitutive granularity does not necessarily yield the maximal object.
Figure 7.
Trans-Granular Multiple Instantiation and the Distinction of Instance Granularity and Type Granularity.
A) Left: Compositional partitions of a constitutively organized idealized multicellular organism into its constitutive object parts. Four partitions are shown: (i) into organs (f); (ii) into organ cells (e); (iii) into organelles (c,d) of organ cells; and (iv) into organelle molecules (a,b). Right: Compositional partitions of a cumulative-constitutively organized idealized multicellular organism into its constitutive object parts. The same corresponding four partitions are shown: (i) into organs (j) alongside with cells (i) and extracellular molecules (g,h), both of which are not part of any organ; (ii) into organ cells (q) and extracellular molecules (o,p) that are part of some organ, organelles (m,n) that are part of cells which are not part of any organ, and cellular molecules (k,l) that are neither part of any organ nor any organelle; (iii) into organelles (v,w) of organ cells and molecules (t,u) that are part of these organ cells but not part of any organelle, as well as molecules (r,s) of organelles of cells which are not part of any organ; and (iv) into organelle molecules (x,y) that are part of organ cells. B) Left: The instance granularity tree of constitutively organized bona fide objects based on the corresponding four partitions. Each partition constitutes a cut in the instance granularity tree (Cut I–IV) and thus an instance granularity level. Contrary to cumulative-constitutively organized material entities, particular instances of the same type of material entity do not belong to different cuts and thus are restricted to a single level of instance granularity. The types' extensions do not transcend the boundaries between instance granularity levels. Right: The instance granularity tree of cumulative-constitutively organized bona fide objects based on the corresponding four partitions. Particular instances of the same type of material entity, like for instance of the type MOLECULE, belong to different cuts and thus different levels of the respective instance granularity. In other words, the extension of the type MOLECULE transcends the boundaries between instance granularity levels. C) Left: The constitutive instance granularity tree that results from the corresponding four partitions can be directly transformed into the respective type granularity tree – no sortation required since they are topologically identical. Right: The cumulative constitutive instance granularity tree that results from the corresponding four partitions cannot be directly transformed into or mapped upon the respective type granularity tree. However, by (i) following the simple and intuitive rule of sortation-by-type (i.e. a type occupies the same granularity level as its finest grained instance) and by (ii) applying a more complicated granularity scheme (Vogt 2010), one can infer a type granularity tree. Unfortunately, this results in types of entities belonging to type granularity levels for which BFO provides no respective categories as templates for granularity specific ontologies (here marked ‘???’). For instance when looking at the cellular level, a cellular ontology that is based on BFO provides no category for molecules that are not part of any cell, since they are neither a cell (i.e. BFO's ‘object’), nor a cell aggregate (i.e. BFO's ‘object aggregate’) or fiat cell part (i.e. BFO's ‘fiat object part’), nor any of the additional categories of the extended BFO. (modified from [19]).
Figure 8.
A Cluster of Cells at the Molecular and the Cellular Level of Granularity.
Left - A material entity that is a cluster of molecules at the molecular level of granularity. The molecule cluster constitutes two cells embedded in extracellular matrix (ECM). The two cells are connected with each other via a cell-cell junction. The molecules form a molecule cluster since they are connected with each other via molecular bonds. Right - The same material entity at the cellular level of granularity in which it is a cell cluster with portion of ECM cluster. The cell molecules constitute two cells that are connected via a cell-cell junction, thus forming a cell cluster. The ECM molecules form a portion of ECM that is a fiat entity.
Table 4.
Three Types of Material Entity and their different Granularity Representations at Four Levels of Granularity.
Figure 9.
Taxonomy of Top-Level Categories of Constitutively and Cumulative-Constitutively Organized Material Entities.
A taxonomy of top-level categories of material entity and important subcategories that can be distinguished in constitutively and cumulative-constitutively organized material entities. Black boxes indicate Basic Formal Ontology (BFO) categories of material entity, dark grey boxes the additional categories suggested by [4], white boxes additional categories required for accommodating all cumulative-constitutively organized material entities, and shaded grey boxes examples for specific subcategories involving portions of matter as building blocks.
Figure 10.
Integrated and Simplified Taxonomy of Top-Level Categories of Material Entity.
A taxonomy of top-level categories of material entity and important subcategories that can be distinguished in constitutively and cumulative-constitutively organized material entities. By introducing the category ‘material entity aggregate’ one can reduce the number of foundational categories that exhaustively cover all possible types of constitutively and cumulative-constitutively organized material entities to four. All other categories represent additional categories that are organized into three hierarchical levels and subsumed under the foundational category ‘material entity aggregate’. All clusters of material entities are subsumed under ‘material entity cluster’ and all groups under ‘material entity group’ respectively. Black boxes indicate Basic Formal Ontology (BFO) categories of material entity, dark grey boxes the additional categories suggested by [4], and white boxes additional categories required for accommodating all cumulative-constitutively organized material entities.
Figure 11.
Sortation by Type using Categories based on Granular Representation.
Left: Following the rule of sortation-by-type and applying a more complicated granularity scheme (Vogt 2010) one infers this type granularity tree from the instance granularity tree shown in Fig. 7. This results in types of entities belonging to type granularity levels for which BFO provides no respective categories as templates for granularity specific ontologies (here marked ‘???’): BFO (version 1.1) provides no category for molecules that are not part of any cell, since they are neither a cell (i.e. BFO's ‘object’), nor a cell aggregate (i.e. BFO's ‘object aggregate’) or fiat cell part (i.e. BFO's ‘fiat object part’). Right: By applying the notion of granular representation and the here proposed categories of portion of matter and portion of matter aggregate, the transformation of the instance granularity tree into a type granularity tree can be completed. With these additional categories and the notion of granular representation one can account for the effects of trans-granular multiple instantiation in cumulative-constitutively organized material entities.