Granularity dependence of <i>bona fide</i> boundaries of some object clusters.

<p><b>Left:</b> An object cluster consisting of six object entities. This cluster is exclusively demarcated by <i>bona fide</i> boundaries, and so is any of its sub-clusters (e.g. the two sub-clusters, each consisting of three object entities (in light-grey and in dark-grey). <b>Right:</b> The object cluster consisting of six object entities constitutes an object at a coarser granularity level. This object is demarcated from its surrounding complement by a <i>bona fide</i> boundary. Contrary to the finer granularity level, however, within this coarser level the two sub-clusters cannot be demarcated by <i>bona fide</i> boundaries anymore: The adherence relation between the objects involved (light-grey and dark-grey) at the finer level maps to a coherence relation at the coarser granularity level. Therefore, the respective parts are demarcated by a <i>fiat</i> boundary<i>^mat</i>. <b><i>Fiat</i></b><b> boundary</b><b><i>^mat</i></b><b>:</b> demarcates <i>fiat</i> parts of a material entity.</p

Integrated and Simplified Taxonomy of Top-Level Categories of Material Entity.

<p>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 <i>foundational categories</i> that exhaustively cover all possible types of constitutively and cumulative-constitutively organized material entities to four. All other categories represent <i>additional categories</i> 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. <i>Black boxes indicate Basic Formal Ontology (BFO) categories of material entity, dark grey boxes the additional categories suggested by </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030004#pone.0030004-Vogt1" target="_blank">[4]</a>, <i>and white boxes additional categories required for accommodating all cumulative-constitutively organized material entities.</i></p

Three Foundational Types of Spatio-Topological Relations between Material Entities (from [4]).

<p>Three Foundational Types of Spatio-Topological Relations between Material Entities (from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030004#pone.0030004-Vogt1" target="_blank">[4]</a>).</p

Definitions of the basic types of material entity of the Basic Formal Ontology (BFO version 1.1).

<p>Definitions of the basic types of material entity of the Basic Formal Ontology (BFO version 1.1).</p

Compositional and spatial partitions.

<p><b>A</b>. A <i>compositional partition</i> of <i>bona fide</i> objects that are situated in a nested fashion (constitutional hierarchy; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018794#pone-0018794-g002" target="_blank">Fig. 2</a>) within <i>bona fide</i> objects of a coarser granularity, which in their turn are, again, situated within <i>bona fide</i> objects of an even coarser granularity. A compositional partition always yields objects that are demarcated exclusively by <i>bona fide</i> boundaries. <b>B</b>. A <i>spatial partition</i> of the same constitutively organized <i>bona fide</i> object into an object aggregate and a <i>fiat</i> object part. <b>C</b>) A <i>spatial partition</i> of a <i>bona fide</i> object resulting in two <i>fiat</i> object parts, one of which in its turn is spatially partitioned again, resulting in two other <i>fiat</i> object parts. <b><i>Fiat</i></b><b> boundary</b><b><i>^mat</i></b><b>:</b> demarcates <i>fiat</i> parts of a material entity; <b><i>fiat</i></b><b> boundary</b><b><i>^immat</i></b><b>:</b> demarcates <i>fiat</i> parts of an immaterial entity (i.e. a hole).</p

Taxonomy of top-level types of constitutively organized material entities.

<p>A taxonomy of top-level types of material entity and important subtypes that can be distinguished in constitutively organized material entities. types that are presently distinguished in the Basic Formal Ontology (BFO) are in dark grey.</p

Sortation by Type using Categories based on Granular Representation.

<p>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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030004#pone-0030004-g007" target="_blank">Fig. 7</a>. 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 <i>granular representation</i> and the here proposed categories of <i>portion of matter</i> and <i>portion of matter aggregate</i>, 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.</p

Definitions of additional Top-Level Categories of Material Entity for the Basic Formal Ontology (from [4]).

<p>Definitions of additional Top-Level Categories of Material Entity for the Basic Formal Ontology (from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030004#pone.0030004-Vogt1" target="_blank">[4]</a>).</p

A Cluster of Cells at the Molecular and the Cellular Level of Granularity.

<p>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.</p

Three foundational types of spatio-topological relations between material entities.

<p>Three foundational types of spatio-topological relations between material entities.</p