This page covers some well-known literature on different approaches towards handling the challenges of the BFO:MaterialEntity class and its subclasses.

The slides for the talk are attached here:

• The authors tackle BioTop (a granularity-independent top-domain ontology for biomedicine) and align it with BFO. The trouble appears exactly at BFO’s third level of material entities: Object, ObjectAggregate, and FiatObjectPart.

• Many biomedical entities simultaneously satisfy the criteria for more than one of these MaterialEntity subclasses.

• Any self-connected physical object can also be viewed as a mereological sum of molecules, atoms, and other fundamental components. So a single continuant may satisfy both self-connected and some sum of separate objects, depending on which parts you attend to.

• Problem of Connectivity: Sometimes the population of individuals is physically connected (e.g., biofilms, aggregations of unicellular organisms), while at other times they are scattered (e.g., humans), but you still want to have only 1 class of Population.

• Siamese twins are a conjoined double organism, as what a "whole" satisfies BFO's Object criteria.

• However, each twin being a FiatObjectPart of the organism, they would be an independent Object after the surgery.

• Similar issues arise for symbiotic organisms, organs connected by continuous ducts/vessels, etc.; there is no clean fiat or bona fide boundary at a given granularity level.

• Connectedness and fiatness are inherently granularity-dependent.

  • Different physical resolutions or domain descriptions result in the entity belonging under different subclasses of MaterialEntity.

• BFO insists on subclasses of MaterialEntity to be disjoint. An ontology (especially upper-level ones) should allows for some version of unionization between these classes; something beyond the "X 'or' Y (but not sure which)" statement.

• Conclusion: Upper-level ontologies must be neutral regarding granularity.

• BioTop ignores BFO's 3rd level subdivision.

• Object, ObjectAggregate, and FiatObjectPart become local modeling tools, after you have fixed parameters for time and ontology.

• Final Solution: Don’t ask BFO’s Object/ObjectAggregate/FiatObjectPart to be global, granularity-independent, identity-determining categories. Use them only in small, context-bound pieces of the ontology where granularity is fixed. At the integrative “top domain” level, stay at MaterialEntity and maintain granularity neutrality.

  • ⚠️ Comment: Is this a possible way to handle our problems in IOF? I don't think so. We have a foundry of connected ontologies, where, across them or even within one of them, we might encounter the problems mentioned above.

    • Perhaps, we can treat everything as material entity, and change the subclasses to some SpecificallyDependentEntity form subclass that would be used whenever needed.

1. BFO’s Object, ObjectAggregate, and FiatObjectPart trichotomy should not be global in an integrative IOF-like upper layer. A precedent for treating those categories as granularity-relative “representation types”, only enforced within specific modules.

2. BFO's MaterialEntity should be the only thing that we put things under. Treat Object, ObjectAggregate, and FiatObjectPart as some forms of SDC that material entities can possess depending on the granularity level of the domain/module.

• BFO's three-way classification of Object, ObjectAggregate, and FiatObjectPart under MaterialEntity is not exhaustive for representing all forms of material entities in the world.

• Other types must be introduced to cover the gap in BFO; types that are both exhaustive and mutually disjoint.

• The authors propose six new aggregate subtypes based on distinct topological structures:

  • They begin by adding 2 new aggregate types (sibling classes to the 3 of BFO):

    • FiatObjectPartAggregate: A mereological sum of fiat object parts that together form a whole, but that are not demarcated from one another or from the exterior by bona fide boundaries.

      • Some collectives consist of multiple parts, but not of complete objects, and therefore cannot be classified as object aggregates.

      • A FiatObjectPart is not an Object, and a group of fiat parts is not an ObjectAggregate.

      • Paper Examples: the dorsal surfaces of all organs in a region, all right halves of a group of organisms, the interior surfaces of all bones in a limb.

      • IOF Example: all the bonding surfaces of components before assembly. The welding surfaces are fiat parts, not objects.

      • IOF Example: the set of all left halves of some casing in a shipment.

      • IOF Example: All the threaded portions of a batch of bolts.

    • ObjectWithFiatObjectPartAggregate: A mereological sum consisting of at least one object and at least one fiat object part, where the aggregate as a whole is not a single object, nor a pure fiat object part, nor an object aggregate.

      • Paper Example: When partitioning a multicellular organism, at a given cut, you may have: Organs (objects), Cells not belonging to any organ (objects at a different level), Spatially demarcated regions (fiat object parts), Extracellular matrix (portion of matter, but formally falls into the "fiat-part-like" category).

        • These mixed cuts consist of both bona fide objects and fiat object parts.

      • IOF Example: motor + drum + mounting bracket part of a chassis + rear plate opening part.

      • IOF Example: pallet + 3 pump housings + the inlet-port part of each housing that will be inspected separately.

      • IOF Example: a shipment of several complete metal shafts and test-sample cores removed from larger billets.

      • IOF Example: a flagged batch of seven products and a product with a damaged region.

• The next step is to divide each of these aggregate classes by distinguishing between Clusters and Groups; Topologically Coherent Aggregates vs. Merely Spatially Proximate or Socially/Causally Clustered.

  • This leads to 6 classes: ClusteredObjectAggregate, GroupedObjectAggregate, ClusteredFiatObjectPartAggregate, GroupedFiatObjectPartAggregate, ClusteredObjectWithFiatObjectPartAggregate, GroupedObjectWithFiatObjectPartAggregate.

  • This is significant for IOF because industrial aggregates behave differently depending on topology, adhesion, mixture, or spatial relation.

• BFO's three original MaterialEntity subclasses assume a strict constitutive hierarchy, where every granularity level nests into the next like Russian Dolls.

• However, in biology and industry domains, we need a cumulative constitutive organization, where not all parts of a given type may neatly fit into a next-level whole.

• Therefore, BFO must expand its MaterialEntity subclasses to cover:

  • New types of aggregates,

  • Representation of entities at different levels of granularity,

  • and constitutive vs. cumulative granularities.

• A continuation of Vogt's 2011 paper.

• Vogt argues that even after the new categories were introduced, BFO still cannot model the full complexity of Cumulative-Constitutively Organized Material Entities.

• Cumulative Constitutive Organization has 2 forms:

  1. Constitutive Granularity

     • a.k.a, the simple hierarchy

     • Every part at one level belongs to some whole at the next level.

       • molecules -> Cells -> Organs -> Organism

     • This is what BFO implicitly assumes.

  2. Cumulative Constitutive Granularity

     • Reality for most systems

     • Many parts do not belong to any whole at the next level

       • For example, free cells in blood, molecules appearing at multiple levels of granularity, or aggregates that mix parts from different granularity levels.

       • More IOF-related example: Certain subassemblies belong to multiple hierarchies simultaneously.

     • BFO's MaterialEntity subclasses are not sufficient for these systems.

• Even the extended classes from the 2011 paper fail to cover all real-world cases because the cumulative constitution allows for:

  • types existing at multiple granularity levels simultaneously

  • entities whose parts span different levels

  • mixture or cluster portions not covered by any defined classes.

• A single type of MaterialEntity can appear in different granularity levels, with different structural roles, across different organizational layers.

• Vogt’s 2012 paper is the first to give this phenomenon a name and formal analysis.

• The proposed solution is adding the following categories as classes under MaterialEntity:

  • Portions of matter

  • Aggregates with portions of matter as members

  • Entities mixing object-like and portion-like constituents

  • Cross-granularity aggregates

• The proposal asks for a reorganization of the MaterialEntity subclasses under a new umbrella.

  • MaterialEntityAggregate -> Cluster vs. Group -> Many more subclasses such as:

    • MaterialEntityCluster (topologically coherent)

    • MaterialEntityGroup (loosely associated)

    • ObjectAggregateWithFiatPartComponents

    • PortionOfMatterAggregate

    • Mixed-LevelAggregate

• ⭐ This indicates that classification depends on the granularity level being used.

  • This means that the same real-world instance may be classified into different BFO categories in different modules.

    • At one granularity, it may be "Cell," at another "Tissue Component," and at another "Portion of Matter."

• This is one of the most important responses to the Vogt papers, and it directly affects how IOF should think about Object vs. Object Aggregate vs. Artifact, identity, and granularity.

• Agrees with BFO's three MaterialEntity subclasses not being exhaustive.

• Rejects the idea that BFO should rely on granularity structure to define its categories.

• Introduces Causal Unity as the "real" ontological basis for classifying material entities.

  • Proposes 3 types of causal unity: Unity via an Enclosing Membrane, Unity through Functionally Coordinated Process, and Unity through Homogeneity.

  • Mentions these are not exhaustive.

• Acknowledges the need to add new classes: "BFO or its conformant domain-ontologies will in due course need to recognize also other sub-universals of material entity, in addition to object, object aggregate, and fiat object part."

Motivation

• Scientists discuss the Natural Units of Matter (e.g., cells, molecules, organisms, artifacts, planets), but these are not defined solely by granularity. Rather, they are defined by some Causal Unity.

  • This is his motivation for shifting from Vogt's geometric/topologically centered structure to a functional/causal one.

• "A material entity is something causally relatively isolated, possessing some form of internal causal integration."

• CU1: Physical Covering - Casing/unity via an enclosing membrane

  • e.g., most organs, many biological objects, some artifacts

• CU2: Internal Causal Integration - Functionally Coordinated Processes

  • e.g., machines, most artifacts, some biological wholes

• CU3: Portion of Matter - Causal Unity through Homogeneity

  • e.g., solid undivided chunks of matter, rock, soil, metal billet

• "An entity is an 'object' when its internal causal unity satisfies certain threshold conditions..."

  • If you try to move part b from inside to outside, the object will move in coordination or be damaged

  • Causal changes in one part affect others without some mediation of the exterior.

• For example, a collection of unassembled components lacks coordinated causal unity; therefore, it's not an object. However, a fully assembled artifact regains its causal unity and becomes an object.

• ⭐This is a clear example of BFO rejecting the Identity-by-parts principle!

• Smith states: "A portion of matter is anything that includes elementary particles among its parts."

  • This seems a bit too vague and tricky!

• Portions of matter, such as fluids, powders, bulk materials, etc. are not aggregates, nor objects.

• Membership-Based Identity (identity-by-parts) is rejected; emphasizing causal unity.

• The change between ObjectAggregate and an Artifact can be explained through the following:

  • Before assembly: no causal unity → OA

  • After assembly: causal unity → Object/Artifact

  • This is not a contradiction → it's an ontological transformation caused by a process

  • ⚠️ BUT WHERE IS CAUALITY!!!

• The Causal Unity is a great way to model the Processes of Aggregation and Disaggregation.

  • If a Process of Aggregation results in establishing causal unity, identity changes

  • If a Process of Disaggregation destroys causal unity, identity changes

  • Aggregating homogeneous portions of matter → identity is not individual-based but mass-based

• Smith rejects classifying material entities based on granularity, and he's not wrong to make this claim.

• However, he does not resolve the cross-granularity representation problem.

  • For Smith, a cell is always an object, and his system cannot change a cell's type based on module representation.

  • For him, a class cannot shift between MaterialEntity subclasses depending on the modeling perspective! BUT THIS IS EVERYTHING WE ARE HAVING PROBLEMS WITH!

  • Smith does not offer a mechanism for cross-granular or multi-perspective classification.

• For Smith, interoperability comes from shared universals, and granularity differences should be handled elsewhere, not by creating new subclasses.

  • BUT WHERE?

• So, all biology ontologies must reuse the same universal "cell."

  • Differences in perspective must be encoded not through MaterialEntity subtypes, but through Roles, Functions, dispositions, Domain-Specific Qualities, or perhaps through cross-modular properties (e.g., 'granularPartOf', constructivelyRelatedTo), or even annotations???

• This also applies to ontologies with multiple granularity levels. Since, according to Smith, the class hierarchy stays granularity-neutral!

• Domain ontologies provide multiple "views" of the same entity, not multiple classes.

  • But this does not address how to coordinate different granularity-dependent axioms;

  • Or how to validate across modules;

  • Or how to enforce cross-module consistency;

  • Or how to represent multi-level classification.

• This paper differs somewhat from the others, as it focuses on mechanisms (processes) instead of material entities alone.

• Allen argues that mechanisms cannot be represented correctly at a single level or from a single perspective. They require multiple representational layers that do not perfectly align.

• The same biological mechanism can be represented at the molecular, cellular, tissue, or organismal level.

  • And Allen claims that these representations are not reducible to one another.

• In manufacturing, we have assembly mechanisms, component mechanisms, and material mechanisms, all of which describe the same artifact in different ways.

• ⭐ Different representational levels use different primitives, different parthood relations, and different identity assumptions!

• Parthood is layer-dependent (as discussed above).

• Mechanism descriptions only invoke "relevant" parts.

  • Mechanism descriptions are intentionally incomplete because scientists decide on which parts matter for their explanatory task, and therefore, pick different sets of parts for different modules/levels.

    • For example, a thermodynamic module for describing a car examines different parts compared to those that a kinematic module focuses on.

  • "The criteria of relevance shape the ontology, not the underlying metaphysics."

• Mechanisms involve different types of relations at different levels:

  • structural vs. functional relations

  • dispositions vs. causal connections

  • organization vs. behavior

  • configuration vs. interaction

  • These relations change classification.

  • Comment: Smith only addresses a small portion of these in his paper.

• Ontologies must support multiple models/views aligned to different tasks.

  • e.g., explanation, simulation, diagnosis, design, control

  • Each view should:

    1. pick its own entities (doesn't align with Smith)

    2. pick its own "parts"

    3. ⚠️ pick its own identity criteria

    4. Pick what counts as aggregates

    5. define roles contextually

  • This approach aligns with Vogt and contradicts Smith

• These different views must be linked via explicit "correspondence relations."

  • Allen insists on using relations like:

    • 'abstractionOf'

    • 'implementationOf'

    • 'refinementOf'

    • 'realizes'

    • systemOf'

  • He argues that interoperability comes between representations, not in the classification!

• This paper is the foundational statement of a Semantic de dicto Theory of Vagueness, grounded in a formal account of granular partitions.

• There are no vague objects; all objects in reality have crisp boundaries.

  • Vagueness arises only from the mapping between expressions and reality.

• A vague name or predicate has many "equally good" candidate referents or extensions.

  • These candidates correspond to multiple granular partitions (e.g., multiple projections of the term "cell" onto reality).

• The theory provides a new version of Supervaluationism, replacing truth-value gaps with context-dependent projections.

  • Cells are artificially carved-out regions of reality, used for some particular representation (region-based).

• ⭐ This is not about fuzziness or degrees, but about multiple crisp alternatives under contextual constraints.

• A Partition is a system of "cells" arranged in a possibly nested tree-like structure. Like shining a set of flashlights onto the world, each cell projects onto some region or object.

  • Pt = (A, P, L)

    • A = the system of cells (tree structure)

    • P = the projection relation (cells -> objects)

    • L = the location relation (objects -> cells)

• The cell structure (A) must satisfy:

  1. Subcell relation ⊆ is reflexive, transitive, and antisymmetric.

  2. Chains of nested cells are finite (atomism).

  3. If two cells overlap, one must be a subcell of the other.

  4. Each partition has one unique maximal (root) cell.

• The consequence is that every granular partition can be represented as a tree.

1. Projection presupposes Location: L(o, z) -> P(z, o)

2. Transparency - Successful Projection implies Location: P(z, o) -> L(o, z)

3. Therefore, we can say L(o, z) <-> P(z, o)

4. Each cell projects onto at most 1 object: P(z, o₁) ⋀ P(z, o₂) -> o₁ = o₂.

5. Each object is located in at most 1 location: L(o, z₁) ⋀ L(o, z₂) -> z₁ = z₂.

6. Every cell projects onto something: Z(z, A) -> ∃o L(o, z)

• ⭐ A crisp granular partition Pt (shown above) satisfies all the axioms above.

• A vague partition relaxes the idea that there is a single mapping, and we obtain many projection/location pairs, each representing a possible crisping.

  • Pt_v = (A, P_v, L_v)

    • Where P_v and L_v are sets of projection/location relations.

• Each projection has a unique corresponding location

• Projection and Location are functional relations (as mentioned for crisp partitions above).

• There are no empty cells under any crisping (as shown above).

• Each pair (P_i, L_i) defines a crisping:

  • Pt_i = (A, P_i, L_i)

  • And the domain of the vague partition is the mereological sum of the domains of all crisps.

• A judgement is a pair: J = (S, Pt)

  • where S is a sentence, and Pt is the partition used to interpret it.

• For vague partitions Pt_v:

  • J is supertrue if it is true with respect to all crispings Ptᵢ.

  • J is superfalse if it is true with respect to none of the crispings.