Ontology by Be

• Ontologically, BE expresses
• Functional morphemes used with BE in ontology
• What Is NOT Used with BE in Ontology
• Copula
• Ontological Scope of BE
• Ontological Uses of BE (Closed Set)
• Examples of the 6 Ontological Uses of BE
• Co-occurrences and Co-variants of BE
• Articles / Determiners — Class vs Instance Control
• Quantifiers Used with BE
• Predicative (Non-Relational) Properties Expressed by BE
• Is Identification of More Than One Entity Universal?
• Are All Classes Universal?
• Class: Within Taxonomy and Outside Taxonomy
• Taxonomy for Human
• Are All Biological Taxonomic Ranks Classes?
• Relation between Essence and BE
• Use of Base Verb Forms in Ontology
• Classes in WordNet
• BE / Class Relations in ConceptNet 5 and WordNet
• Are All Classes Grounded in BE?
• What Are the Essences That Form a Class?
• Essences of Classes Not Grounded in BE
• Are All Nouns “By BE”?
• Are Parts of Speech Other Than Nouns “By BE”?
• Classification of Nouns by BE (Ontological Classification)
• Part–Whole vs BE Relations
• Inseparable Parts of a Whole That Are Treated as Classes
• Classes of Matter (Ontological Classification)
• Classes in Biology and Biological Taxonomy
• Matter Taxonomy by BE (Is-a Only)

[Instance/Class] + BE + [Article] + [Class/Category]

Inflected forms of BE (be, is, are, was, were, been, being) can be used to express:

BE →

• Identity
• Class / Category / Type
• Predicative (non-relational) properties
• Definition / equivalence
• State (non-possessive)
• Existence only via “there is / there are”

Ontologically, BE expresses:

identity
class membership
category inclusion
equivalence

Examples:
An electron is a lepton.
Human is a mammal.

These are identity statements, not behaviours.

Functional morphemes used with BE in ontology:

Functional morphemes do not add content; they constrain interpretation.

Copula: is, are
Articles: a, an, the, Ø
Prepositions: of, as, in
Quantifiers: a, every, some
Relativizers: that, which
Negation: not

BE carries identity.
Functional morphemes control how that identity is interpreted.

What Is NOT Used with BE in Ontology

❌ Lexical verbs (do, make, act)
❌ Adverbs of manner (quickly, slowly)
❌ Possessives (my, his)
❌ Modal intentions (want, try)
Because BE is non-actional.

Copula

Copula means:
a grammatical element (usually a verb) that links a subject to its identity, category, or property — without expressing action.
That is the core meaning.

Subject ──copula──▶ Predicate (what it is)

English copula forms:
be, is, are, was, were, been, being

A copula links a subject to an identity, category, or predicative property — not to possessed or constituent properties.

Ontological Scope of BE

Core Principle

BE operates primarily on the Particular–Universal axis.

It answers:

• What is this?
• What kind of thing is this?

Primary Domain of BE

(Particular–Universal)

BE is used to relate an entity to:

1. A Universal (Class / Category / Type)

   • Particular → Universal
     
   • Universal → Universal
     

2. Itself (Identity)

   • Particular → Particular
     

Examples:

• Prasanth *is** a Human*
  
• Human *is** an Animal*
  
• Prasanth *is** Prasanth*

Secondary but Ontology-Safe Uses of BE

These do not introduce new entities and do not imply part–whole or action.

Predicative Properties

• Qualitative, non-relational predicates

Examples:

• Atom *is** neutral*
  
• Crystal *is** periodic*

States

• Time- or condition-indexed, non-possessive

Examples:

• Material *is** solid*
  
• System *is** idle*

These map an entity to a predicate space, not to another entity.

What BE Is Never Used For

❌ Part–Whole relations (HAS)

❌ Behaviour or change (DO)

❌ Function or purpose (WHY)

❌ Causation or interaction

Final Ontological Rule

BE answers “What is it (as such)?”

It never answers:

• What does it have?
• What does it do?
• Why does it exist?

One-Line Anchor

BE lives on the Particular–Universal axis

and never crosses into Part–Whole or Action.

Entity, Identity, Class, Category, Type
all ultimately organize reality along the axes of
Part–Whole and Particular–Universal.

Ontological Uses of BE (Closed Set)

In ontology, BE is used only for the following six cases:

1. Identity

   • Self-identity or equivalence

2. Class / Category / Type

   • is-a relation (instance–class or class–class)

3. Predicative Properties (Non-Relational)

   • Qualitative, essential, or definitional predicates
     
   • No parts, no possession, no relations

4. Definition / Equivalence

   • Conceptual or stipulative identity

5. State (Non-Possessive, Non-Relational)

   • Time-indexed condition of the same entity
     
   • No action, no interaction

6. Existence

   • Only via the existential construction
     
     • “there is / there are”

--

Explicit Exclusions

BE does NOT express:

• Parts or composition
• Possession or attributes-with-bearer
• Behaviour or action
• Function or purpose
• Causation
• Relations between distinct entities

--

Summary

If a statement does not answer

“What is it?” or “Is it?”,

BE must not be used.

Examples of the 6 Ontological Uses of BE

Below are clear, minimal examples for each allowed use of BE in ontology.

1. Identity

(Self-identity or equivalence)

• Prasanth is Prasanth.
• Water is water.

2. Class / Category / Type

(is-a relation)

• Prasanth is a Human.
• Human is an Animal.
• Electron is a Lepton.

3. Predicative Properties (Non-Relational)

(Qualitative, no parts, no possession)

• Atom is neutral.
• Human is mortal.
• Crystal is periodic.

❌ Not allowed here:

• Atom is electrons (part–whole error)

4. Definition / Equivalence

(Conceptual or stipulative identity)

• A bachelor is an unmarried man.
• Water is H₂O. (definitional reading)

5. State (Non-Possessive, Non-Relational)

(Time-indexed condition, no action)

• The material is solid.
• The system is idle.
• The metal is molten.

⚠️ Still BE, not DO, because no action occurs.

6. Existence

(Only via existential construction)

• There is an electron in the atom.
• There are humans on Earth.
• There is a defect in the lattice.

Contrast: Incorrect Uses of BE

❌ Atom is electrons → should be HAS

❌ Human is organs → should be HAS

❌ Electron is moving → behaviour → DO

❌ Transistor is switching → function → WHY

Reminder

BE answers only:

What is it? / What kind is it? / Is it so?

Anything else requires HAS, DO, or WHY.

Co-occurrences and Co-variants of BE

(Functional / Closed-Class Morphemes Only)

This list includes only functional (closed-class) morphemes that
co-occur with or constrain the meaning of BE in ontological statements.
No lexical (open-class) items are included.

1. Core Copular Forms (BE Variants)

These are inflectional variants of the same verb:

• be
• is
• are
• was
• were
• been
• being

Role:

• Carries tense, number, aspect
• Does not add ontological content by itself

2. Articles / Determiners (Class vs Instance Control)

These are critical for ontology.

• a / an → instance-of (existential, singular)
• the → definite / unique individual
• Ø (zero article) → class-level or generic universal

Examples:

• Prasanth *is a** Human* → instance
• Human *is Ø** animal* → class
• The Sun *is a** star* → unique individual

3. Quantifiers (Logical Force)

Functional determiners that alter scope.

• every / each → universal (∀)
• some → existential (∃)
• no → negated existence
• all → collective universal

Examples:

• Every human *is** mortal*
• No human *is** immortal*

4. Negation

• not

Role:

• Class exclusion
• Predicate denial

Examples:

• A human *is not** a reptile*
• This material *is not** solid*

5. Prepositions (Restricted, Ontology-Safe Set)

Only those that do not introduce possession or action.

• of → classification / definition
• as → role / interpretation
• in → membership (metaphorical, informal)
• among → set membership (plural)

Examples:

• Human *is** a member of Mammalia*
• Prasanth *is** treated as an instance*

⚠️ “in / within” are acceptable linguistically, weak ontologically.

6. Existential Marker (Special Construction)

• there

Used only with BE to assert existence.

Examples:

• There *is** an electron in the atom*
• There *are** defects in the lattice*

Ontological role:

• Explicit existential claim (∃)

7. Relative Markers (Definition / Restriction)

• that
• which
• who (for persons)

Used to restrict or define classes.

Examples:

• Human *is** an animal that is rational*
• A lattice *is** a structure which is periodic*

8. Aspectual / Modal Function Words (Boundary Case)

These do not change ontology, only modality or temporality.

• to (infinitive marker)
• being (participial BE)
• been (perfect aspect carrier)

Examples:

• To *be** human is to be mortal*
• Having *been** molten, the metal is solid*

9. Explicit Exclusions (Not Co-occurrences of BE in Ontology)

These are not allowed with BE for ontological claims:

• possessives (my, his, their)
• action auxiliaries (do, does, did)
• lexical verbs (have, make, act)
• adverbs of manner (quickly, slowly)

Final Closed Summary

Functional / closed-class morphemes co-occurring with BE:

• Copula forms: be, is, are, was, were, been, being
• Articles: a, an, the, Ø
• Quantifiers: every, each, some, no, all
• Negation: not
• Prepositions: of, as, in, among
• Existential marker: there
• Relativizers: that, which, who
• Aspectual markers: to, been, being

Canonical Rule

BE carries identity.

Functional morphemes constrain how that identity is read.

This list is closed and sufficient for ontological use.

Articles / Determiners — Class vs Instance Control (with BE)

Articles and determiners are functional (closed-class) morphemes that
control whether a BE-statement is read as Class-level (universal) or
Instance-level (particular).

They do not change ontology by themselves; they fix the scope.

Core Principle

BE gives identity.

Articles / determiners decide whether that identity is universal or particular.

Determiner → Ontological Reading Map

Canonical Examples with BE

Instance-Level (Particular)

• Prasanth is a Human.
  
  → one instance of the class Human

• The Sun is a star.
  
  → unique individual (definite)

• This human is Prasanth.
  
  → deictic, specific instance

Class-Level (Universal)

• Human is Ø animal.
  
  → the class Human belongs to the class Animal

• Humans are mammals.
  
  → generic plural = universal

• Every human is mortal.
  
  → explicit universal (∀)

Negative Class Statements

• No human is immortal.
  → universal exclusion

What Articles Do Not Do

Articles / determiners do not:

• introduce parts (HAS)
• introduce behaviour (DO)
• introduce function (WHY)

They only fix scope.

Minimal Rule (Keep This)

BE → identity / classification Article / Determiner → instance vs class

Or in words:

Change the article, and you change the ontological level —
without changing the verb.

One-Line Anchor

Articles are the switch that moves BE

between particular and universal.

Quantifiers Used with BE (Ontology-Relevant, Closed Class)

This list includes only functional / closed-class quantifiers
that can co-occur with BE in ontological statements.
Lexical numerals and vague expressions are excluded.

1. Existential Quantifiers (∃)

Used to assert existence or instance membership.

• a / an
  
• some
  
• there is / there are (existential construction)

Examples:

• Prasanth *is a** Human.*
  
• There *is** an electron in the atom.*
  
• Some humans *are** left-handed.*

2. Universal Quantifiers (∀)

Used for class-level or generic truths.

• every
• each
• all (plural collective)
• Ø (zero article) — generic universal

Examples:

• Every human *is** mortal.*
  
• Humans *are** mammals.*
  
• Human *is Ø** animal.* (generic/class level)

3. Negative Quantifiers (¬∃ / ∀¬)

Used to deny class membership or existence.

• no
• none (rare but valid)
• not any (analytic form)

Examples:

• No human *is** immortal.*
  
• None *are** identical.*
  

4. Numerical Quantifiers (Limited, Ontology-Safe)

Only when used to assert cardinality, not measurement.

• one
• two, three, … (small finite numerals)
• many (weak, informal)

Examples:

• There *are** two isotopes.*
  
• There *is** one nucleus.*

⚠️ Use sparingly in ontology.

5. Definiteness-Based Quantification

These imply uniqueness or specificity rather than quantity.

• the → unique individual
• this / that → demonstrative specificity

Examples:

• The Sun *is** a star.*
  
• This human *is** Prasanth.*

6. Quantifiers NOT Used with BE (Ontology)

❌ most

❌ several

❌ few

❌ many of

❌ much

Reason:

• Vague, comparative, or context-dependent
• Better suited to discourse, not ontology

Final Canonical List

Quantifiers compatible with BE in ontology:

• Existential: a, an, some, there is / are
• Universal: every, each, all, Ø
• Negative: no, none
• Cardinal (restricted): one, two, …
• Definiteness: the, this, that

Final Rule

Quantifiers with BE control scope (∃ / ∀ / ¬),

not behaviour, possession, or action.

This list is closed, minimal, and ontology-safe.

Predicative (Non-Relational) Properties Expressed by BE

Core Definition

Predicative properties are properties that

• do not introduce another entity
  
• do not imply possession or part–whole
  
• do not describe action or change
  
• directly characterize what the subject is like
  

Such properties are legitimately expressed by BE.

Ontological Test (Very Important)

A property is predicative (BE-compatible) if:

• It can be stated as:
  “X is P”
• And P does not require another noun/entity

If the predicate requires another thing, BE is not allowed.

Main Classes of Predicative Properties

1. Qualitative Properties

(Intrinsic qualities)

• neutral
  
• solid
  
• liquid
  
• gaseous
  
• rigid
  
• brittle
  
• periodic
  

Examples:

• Atom is neutral
  
• Material is solid
  
• Crystal is periodic
  

2. Essential / Definitional Properties

(Belong to the essence of a class)

• mortal (for humans)
  
• rational (classical definition)
  
• composite
  
• fundamental
  

Examples:

• Human is mortal
  
• Atom is composite
  
• Electron is fundamental
  

3. State Properties (Non-Actional)

(Time-indexed but not behaviour)

• idle
  
• molten
  
• active (state, not action)
  
• dormant
  

Examples:

• System is idle
  
• Metal is molten
  

⚠️ These are states, not behaviours, because:

• no interaction is described
• no change process is specified

4. Modal / Condition Properties

(Still predicative, not behavioural)

• stable
  
• unstable
  
• charged (as state, not process)
  
• neutralized
  

Examples:

• Configuration is stable
  
• Atom is charged
  

5. Definitional Equivalence Predicates

(Conceptual identity)

• identical
  
• equivalent
  
• equal (logical, not numeric comparison)

Examples:

• Bachelor is unmarried
  
• Water is H₂O (definitional reading)

What Are NOT Predicative Properties (BE Forbidden)

❌ Part-based

• Atom is electrons
  → requires HAS

❌ Possessive

• Electron is charge
  → requires HAS

❌ Behavioural

• Electron is moving
  → requires DO

❌ Relational

• Human is taller than X
  → introduces another entity

Diagnostic Rule (Keep This)

If the predicate:

• introduces another entity → ❌ BE
  
• implies possession or part → ❌ BE
  
• implies action or change → ❌ BE
  

Only pure predicates are BE-compatible.

Final One-Line Anchor

BE links an entity to a predicate,

not to another entity.

This is the clean ontological meaning of

predicative (non-relational) properties.

Is Identification of More Than One Entity Universal?

Short Answer

No. Identifying more than one entity does not automatically make it Universal.

Universality depends on scope, not on count.

Cardinality vs Ontological Level

Two different questions must be separated:

1. How many entities are identified? → Cardinality
   
2. At what level are they identified? → Particular vs Universal

Only the second determines universality.

Case Analysis

1. Multiple Particulars (Not Universal)

Identifying many individuals one by one remains particular.

Examples:

• Prasanth, Arun, Sita are humans
  
• Electron₁, Electron₂, Electron₃
  

Logical form:

Human(Prasanth) ∧ Human(Arun) ∧ Human(Sita)

Ontological status:

• Plural particulars
  
• Not universal

2. Universal Identification

Identification becomes universal when a predicate applies to all possible instances of a class.

Examples:

• Human is a mammal
  
• Every human is mortal
  
• Electrons are leptons
  

Logical form:

∀x (Human(x) → Mortal(x))

Ontological status:

• Class-level
  
• Universal

3. Plural Generic (Universal, Not Enumeration)

Sentence:

• Humans are mammals.

Although plural, this is universal, not particular.

Reason:

• Generic statement
  
• Refers to the class as a whole
  
• Does not enumerate individuals
  

Summary Table

Final Rule

Universality comes from scope, not from number.

One-Line Anchor

More than one entity does not create a universal;

only class-level predication does.

Are All Classes Universal?

Short Answer

Yes. All classes are universal.

Why This Is Correct

What a Class Is

A class is:

• A grouping based on shared identity or essence
• A predicate that can apply to many possible instances
• Not tied to any single individual

That makes it universal by definition.

Ontological Clarification

Examples:

• Human → class → universal
  
• Electron → class → universal
  
• Prasanth → individual → particular
  

Logical Perspective

A class corresponds to a predicate:

Class: Within Taxonomy and Outside Taxonomy

Core Claim

A class is always a Universal.

It may exist within a taxonomy or outside a taxonomy.

Taxonomy is an organizational structure;

classhood is an ontological status.

1. Class Within a Taxonomy

Meaning

• The class is placed in a hierarchical system
• Explicit is-a relations exist
• Parent–child (superclass–subclass) relations are defined

Examples (Biology)

Living Being
└── Animal
└── Mammal
└── Human

• Human → class (universal)
• Mammal → class (universal)
• Animal → class (universal)

Ontological Features

• All are universals
• Explicit inheritance of properties
• Taxonomy provides order, not existence

2. Class Outside a Taxonomy

Meaning

• The class exists without being placed in a hierarchy
• No explicit superclass or subclass is specified
• Still a valid universal

Examples

• Tool
• Machine
• Red Object
• Physical Entity
• Semiconductor Material

These are:

• Classes (universals)
• Often cross-cutting
• May overlap multiple taxonomies

Example:

• “Red object” cuts across animals, materials, devices

3. Why Taxonomy Is Optional

Ontological Fact

A class does not require a taxonomy to exist.

• Taxonomy is a human-imposed structure
• Classhood is about predicability over many instances

You can have:

• A class without a taxonomy
  
• But not a taxonomy without classes

4. Comparison Table

5. Relationship to Particulars

• Instances belong to classes
• Classes may or may not be taxonomically placed

Examples:

• Prasanth ∈ Human
  
• Human ∈ Mammal (taxonomy)
  
• “Student” ∈ Human (role-based, non-taxonomic)

6. Final Rules (Keep These)

1. All classes are universals
2. Taxonomy organizes classes; it does not create them
3. A class can exist without taxonomic placement
4. Being outside a taxonomy does not weaken classhood

One-Line Anchor

Class is ontological.

Taxonomy is organizational.

Taxonomy for Human

Biological Taxonomy (Standard Scientific Hierarchy)

• Domain: Eukaryota
  
• Kingdom: Animalia
  
• Phylum: Chordata
  
• Subphylum: Vertebrata
  
• Class: Mammalia
  
• Order: Primates
  
• Family: Hominidae
  
• Genus: Homo
  
• Species: Homo sapiens

Ontological Reading (Aligned with BE)

Each line is an is-a (BE) relation:

• Human is a Mammal
  
• Mammal is an Animal
  
• Animal is a Living Being
  

This is Particular–Universal classification, not part–whole.

Notes on Taxonomy vs Ontology

• All levels above are classes (universals)
  
• No level implies possession or composition
  
• Taxonomy organizes classes; it does not create them

Optional Extensions (Non-Biological, Still Class-Level)

These are classes outside strict biological taxonomy:

• Human is a Social Being
  
• Human is a Cultural Agent
  
• Human is a Rational Animal (classical definition)

These are valid class predicates, but not taxonomic ranks.

One-Line Anchor

Human is a species within a biological taxonomy

and a class within multiple ontological taxonomies.

Are All Biological Taxonomic Ranks Classes?

Answer

Yes. All biological taxonomic ranks are classes (universals).

Ontological Clarification

In biological taxonomy, every rank refers to a universal category whose
instances are organisms. No rank refers to a single individual.

Taxonomic Ranks and Ontological Status

Why Species Is Also a Class

• Species is not an individual
• It is a class whose instances are organisms

Example:

• Prasanth is a human → particular
  
• Homo sapiens → class (universal)

Logical form:

Homo_sapiens(x)

Final Rule

Taxonomic ranks differ only in generality,

not in ontological status.

One-Line Anchor

In taxonomy, everything listed is a class;

only organisms are particulars.

Relation between Essence and BE

Core Statement

BE is the linguistic–ontological operator used to express Essence.

Essence answers:

• What a thing is, by necessity
• What makes it the kind of thing it is

BE is the verb that asserts that essence.

1. What Essence Is (Ontology)

Essence:

• Is necessary, not contingent
• Determines class identity
• Cannot be removed without the thing ceasing to be what it is

Examples:

• Rationality (classical) for Human
  
• Three-sidedness for Triangle
  
• Compositeness for Atom
  

2. How BE Relates to Essence

BE is used to state essential predication

Form:

X IS essentially Y

Examples:

• Human is a rational animal
  
• Triangle is three-sided
  
• Atom is composite
  

In all cases:

• The predicate expresses what the thing must be
• Removing it destroys the identity of X

3. BE vs HAVE in Relation to Essence

Example:

• Human is rational → essence
  
• Human has height → accidental
  

4. Essence vs Accident (Key Distinction)

⚠️ Note:

• Not every BE-statement is essence
• But every essence-statement uses BE

5. Ontological Rule (Critical)

Essence must be expressed using BE,

but BE does not always express essence.

BE can also express:

• Class membership
• Definition
• State

Only when the predicate is necessary and defining does BE express essence.

6. Mapping to Aristotle’s Causes

Final Anchor Statement

Essence is what a thing is;

BE is how ontology says it.

Use of Base Verb Forms in Ontology

Core Rule

Ontology must use base (lemma) verb forms to represent relations.

Therefore, the canonical ontological primitives are:

BE HAVE DO

—not their inflected grammatical forms.

Why Base Forms Are Required

1. Ontology Is Atemporal

• Ontology abstracts away from tense, number, and person
• Inflected forms (is, was, has, does) introduce grammatical noise

2. Base Forms Represent Relations, Not Sentences

• Ontology names relation types
• Language constructs sentences

Correct vs Incorrect Usage

Correct (Ontology-Level Representation)

BE(Prasanth, Human) HAVE(Atom, Electron) DO(Electron, Move)

Incorrect (Grammar-Level Forms)

is / are / was has does

These belong only to natural-language examples.

Relation Between Ontology and Language

• Base forms → ontological primitives
  
• Inflected forms → linguistic realizations

Example:

• Ontology: BE(Prasanth, Human)
• Language: Prasanth *is** a human.*

Final Anchor Statement

Base forms name relations.

Inflected forms express them in language.

Classes in WordNet — Ontologically Aligned

Core Claim

WordNet is primarily an ontology of classes (universals).

It is not an ontology of individual things, but of meanings that function as classes.

What a “Class” Means in WordNet

In WordNet, a class is:

• A noun synset representing a general concept
• A universal, not a particular
• Something that can have instances
• Organized mainly by is-a (BE) relations

So ontologically:

WordNet Class = Universal

Synset = Class Meaning

A synset groups words that share the same class-level meaning.

Example:

{human, homo, man}

This synset denotes the class Human, not any individual human.

Core Class Relation in WordNet

Hypernym / Hyponym

This relation is exactly the ontological BE (is-a) relation.

• Hypernym → Superclass (more general)
• Hyponym → Subclass (more specific)

Example hierarchy:

entity └── living_thing └── animal └── mammal └── human

Every node is a class (universal).

WordNet Top-Level Classes (All Universals)

WordNet begins with very general classes such as:

• entity
• physical_entity
• abstraction
• living_thing
• object
• substance
• group
• event
• state
• act
• possession

All of these are classes, not instances.

Individuals in WordNet (Exceptional Case)

WordNet is not designed to model individuals, but a few appear:

• Proper nouns (e.g., Socrates)
• Unique entities (e.g., Sun, Earth)

Ontological status:

• These are instances (particulars)
• Weakly represented and not central

Rule:

Unless explicitly marked as an instance, a WordNet noun synset is a class.

Alignment with BE / HAVE / DO Framework

WordNet’s backbone is BE.

What WordNet Does NOT Primarily Encode

• Function (WHY)
• Purpose
• Teleology
• Normative roles

These lie outside WordNet’s scope.

Final Ontological Summary

All core noun synsets in WordNet are classes (universals).

They are organized mainly by BE (is-a) relations.

Individuals are secondary and exceptional.

One-Line Anchor

WordNet is a lexical ontology of universals,

structured by class inclusion (BE).

BE / Class Relations in ConceptNet 5 and WordNet

(Ontology-aligned: Identity, Class, Universal relations only)

This list includes only those relations that correspond to BE
(i.e., identity, class membership, category inclusion).
Part–whole, causal, functional, or behavioral relations are excluded.

1. BE / Class Relations in ConceptNet 5

ConceptNet relations are surface-level commonsense links.
Only a small subset corresponds to ontological BE (is-a).

Core BE / Class Relations

1. IsA

   • Meaning: X is a kind of Y
   • Ontology: Class / Category inclusion
   • Example: human IsA animal

2. InstanceOf

   • Meaning: X is an instance of Y
   • Ontology: Particular → Universal
   • Example: Prasanth InstanceOf human

3. DefinedAs (weak BE)

   • Meaning: X is defined as Y
   • Ontology: Definitional equivalence
   • Example: bachelor DefinedAs unmarried_man

⚠️ Notes:

• IsA is the primary BE relation in ConceptNet
• InstanceOf is less frequent but ontologically precise
• ConceptNet mixes ontology with commonsense; BE relations are not strict

2. BE / Class Relations in WordNet

WordNet is a lexical ontology of classes.
BE relations are explicit, formal, and central.

Core BE / Class Relations

1. Hypernym

   • Meaning: X is a kind of Y
   • Ontology: Subclass → Superclass
   • Example: human → mammal

2. Hyponym

   • Meaning: X is a subtype of Y
   • Ontology: Superclass → Subclass
   • Inverse of hypernym
   • Example: mammal → human

3. Instance Hypernym

   • Meaning: X is an instance of Y
   • Ontology: Particular → Universal
   • Example: Socrates → human

4. Instance Hyponym

   • Meaning: Y has instance X
   • Ontology: Universal → Particular
   • Inverse of instance hypernym

3. Alignment Table (ConceptNet vs WordNet)

4. What Is Explicitly NOT BE

These relations exist in both resources but are not BE:

• PartOf / HasA → HAVE
• UsedFor → WHY (Function)
• Causes → DO / CAUSE
• CapableOf → DO
• AtLocation → Relational / contextual
• SimilarTo → Similarity, not identity

5. Ontological Summary

WordNet

• Strict class ontology
  
• BE relations are central and clean
  
• Strong Universal–Particular structure
  

ConceptNet

• Commonsense graph
  
• BE relations exist but are mixed with informal knowledge
  
• IsA is reliable; others need caution
  

Final Anchor Statement

BE relations = IsA / Hypernym / InstanceOf.

Everything else belongs to HAVE, DO, or WHY.

This list is ontology-safe and minimal.

Are All Classes Grounded in BE?

Core Insight

All classes are universals, but not all classes are grounded in BE.

Only some classes arise from identity / essence.
Others are derived by properties, roles, functions, or relations.

Two Kinds of Classes

1. BE-Grounded Classes (Essential / Natural Kinds)

These classes are defined by what an entity is.

Characteristics

• Based on essence or identity
• Stable across contexts
• Support strict is-a (BE) relations
• Form taxonomies

Examples

• Human is an Animal
  
• Mammal is an Animal
  
• Electron is a Lepton
  
• Triangle is a Polygon
  

Ontology sources

• WordNet: Hypernym / Hyponym
  
• ConceptNet: IsA
  

✔ These are BE-classes

2. Non-BE Classes (Derived / Constructed)

These classes are defined by conditions, not essence.

They answer:

Which entities satisfy some criterion?

They are universals, but not natural kinds.

2.1 Property-Based Classes (HAS-derived)

Defined by possessing a property.

Examples

• Red objects
  
• Tall humans
  
• Charged particles
  

→ Property possession (HAS), not identity

2.2 Role-Based Classes (Contextual)

Defined by social or situational roles.

Examples

• Student
  
• Teacher
  
• Driver
  

→ Role depends on context and activity (HAS / DO)

2.3 Function-Based Classes (WHY-derived)

Defined by purpose or use.

Examples

• Tool
  
• Weapon
  
• Sensor
  

→ Purpose, not essence (WHY)

2.4 Relation-Based Classes

Defined by relations to other entities.

Examples

• Things in a room
  
• Neighbors
  
• Connected nodes
  

→ Relational grouping, not identity

Summary Table

Final Rules (Keep These)

BE defines kinds.

Other relations define sets.

All classes are universals,

but only essential classes are BE-classes.

One-Line Anchor

BE answers “What is it?”

Other relations answer “Which ones?”

What Are the Essences That Form a Class?

Core Definition

Essence is what makes something the kind of thing it is.

A class is formed when entities share the same essence.

Only essential features can ground a BE-class.

Essential Criteria That Can Form a Class

1. Kind / Nature (Natural Kind Essence)

The most fundamental essence.

• What it is by nature
• Independent of context or use

Examples:

• Human → rational animal
• Electron → lepton
• Water → H₂O (chemical kind)

✔ Forms natural-kind classes

2. Structural Essence

Defined by necessary internal structure.

• Structure cannot be removed without destroying identity

Examples:

• Triangle → three-sided polygon
• Crystal → periodic lattice
• Atom → nucleus + electrons

✔ Forms formal / geometric / physical classes

3. Constitutive Essence

Defined by what it is made of, necessarily.

Examples:

• Water → H₂O
• Protein → amino-acid polymer
• Semiconductor → doped crystal lattice

✔ Valid when constitution is necessary, not accidental

4. Formal (Definitional) Essence

Defined by exact definition, not by observation.

Examples:

• Bachelor → unmarried man
• Prime number → divisible only by 1 and itself

✔ Strong in logic, mathematics, formal sciences

5. Biological Essence (Species Essence)

Defined by:

• Reproductive continuity
• Genetic coherence
• Evolutionary lineage

Examples:

• Homo sapiens
• Canis lupus

✔ Grounds species-level classes

What Does NOT Count as Essence (Cannot Form BE-Classes)

These may form sets or groups, but not essential classes.

❌ Accidental properties

• Tall humans
• Red objects

❌ Roles

• Student
• Teacher

❌ Functions

• Tool
• Weapon

❌ Relations

• Neighbor
• Member of a group

❌ States

• Sick
• Idle
• Charged (temporarily)

These answer “which ones?”, not “what is it?”

Essence Test (Use This)

A property is essential if:

1. Removing it destroys class identity
   
2. It applies to all instances necessarily
   
3. It supports is-a relations
   
4. It is context-independent
   

If all four are true → Essence

Summary Table

Final Anchor Statement

Essence answers “What must it be?”

Only essence can form a BE-grounded class.

This is the criterion you should apply consistently across your ontology.

Essences of Classes Not Grounded in BE

Core Claim

Classes that are not grounded in BE do not have essence in the strict ontological sense.

They are formed by criteria, conditions, or relations, not by what the entity is.

So the right framing is:

• BE-classes → grounded in essence
• Non-BE classes → grounded in non-essential principles

What Replaces Essence in Non-BE Classes

Instead of essence, these classes are formed by basis principles.
They answer “Which entities qualify?”, not “What is it?”

1. Property-Based Basis (HAS-derived)

Basis Principle

• Possession of a property

Nature

• Accidental
• Removable without destroying identity

Examples

• Red objects
• Tall humans
• Charged particles (temporarily)

Why Not Essence

• Removing the property does not change what the thing is

2. Role-Based Basis (Contextual)

Basis Principle

• Social or situational role

Nature

• Context-dependent
• Time-bound

Examples

• Student
• Teacher
• Patient

Why Not Essence

• A human can stop being a student and remain human

3. Function-Based Basis (WHY-derived)

Basis Principle

• Intended or assigned purpose

Nature

• Teleological
• System-dependent

Examples

• Tool
• Sensor
• Weapon

Why Not Essence

• The same object can change function without changing identity

4. Relation-Based Basis

Basis Principle

• Relation to other entities

Nature

• External
• Relational

Examples

• Neighbors
• Connected nodes
• Members of a group

Why Not Essence

• Relations can change without altering what the entity is

5. State-Based Basis (Temporal)

Basis Principle

• Temporary condition

Nature

• Time-indexed
• Reversible

Examples

• Sick person
• Idle system
• Molten metal

Why Not Essence

• States come and go; identity remains

6. Event/Process-Based Basis

Basis Principle

• Participation in an activity or process

Nature

• Occurrent-based
• Non-substantial

Examples

• Runner
• Speaker
• Processor

Why Not Essence

• These depend on action, not being

Summary Table

Final Rule (Keep This)

If a class can be entered or exited without changing identity,

it is not grounded in essence and therefore not grounded in BE.

One-Line Anchor

BE defines what something is.

Non-BE classes only define when or how it qualifies.

Are All Nouns “By BE”?

Short Answer

No. Not all nouns are grounded in BE.

All nouns name something, but what they name differs ontologically.
Only some nouns correspond to BE-grounded classes (essences).

Key Distinction (Critical)

You must distinguish between:

1. Nouns that name what something *is* → BE-grounded
   
2. Nouns that name conditions, roles, properties, relations, or events → NOT BE-grounded
   

Grammar allows all as nouns; ontology does not treat them equally.

Nouns That ARE Grounded in BE

These nouns denote essences / kinds / natural classes.

Ontological Status

• Universal
• Stable
• Identity-defining
• Support is-a relations

Examples

• Human
• Animal
• Mammal
• Electron
• Atom
• Triangle
• Water

Examples with BE:

• Human is an Animal
  
• Electron is a Lepton
  

✔ These nouns are by BE

Nouns That Are NOT Grounded in BE

These nouns do not express essence.
They express qualification, not identity.

1. Property-Based Nouns (HAS-derived)

Examples:

• Color
• Height
• Charge
• Temperature

Reason:

• These are possessed, not what something is

❌ Not BE-grounded

2. Role-Based Nouns

Examples:

• Student
• Teacher
• Driver
• Patient

Reason:

• Role can change without identity change

❌ Not BE-grounded

3. Function-Based Nouns (WHY-derived)

Examples:

• Tool
• Device
• Sensor
• Weapon

Reason:

• Defined by purpose, not essence

❌ Not BE-grounded

4. State-Based Nouns

Examples:

• Illness
• Rest
• Motion
• Charge (as state)

Reason:

• Temporary, time-bound

❌ Not BE-grounded

5. Relation-Based Nouns

Examples:

• Neighbor
• Member
• Owner
• Part

Reason:

• Defined by relation to something else

❌ Not BE-grounded

6. Event / Process Nouns

Examples:

• Running
• Heating
• Computation
• Collision

Reason:

• These are occurrents, not beings

❌ Not BE-grounded

Summary Table

Final Rule (Keep This)

All nouns are grammatical.

Only some nouns are ontological (BE-grounded).

One-Line Anchor

BE defines kinds.

Language names many things that are not kinds.

This distinction is essential to keep ontology precise and non-confused.

Are Parts of Speech Other Than Nouns “By BE”?

Short Answer

No.

From parts of speech, only certain uses of nouns and adjectives are by BE.

Other parts of speech are generally NOT by BE.

BE is ontological, not grammatical.

Parts of speech are linguistic; only some of their uses align with BE.

Ontological Criterion (Key)

BE applies only when a word answers:

“What is it (as such)?”

If a word answers:

• What does it have? → NOT BE
  
• What does it do? → NOT BE
  
• When / where / how / why? → NOT BE
  

Parts of Speech vs BE (Aligned Table)

1. Nouns — Conditional BE

BE-grounded nouns

• Human
• Mammal
• Electron
• Atom
• Triangle

These express essence / kind.

Example:

• Human is an Animal

NOT BE-grounded nouns

• Student (role)
• Tool (function)
• Height (property)
• Neighbor (relation)
• Running (event)

2. Adjectives — Conditional BE

Only predicative, non-relational adjectives are BE-compatible.

BE-compatible adjectives

• Mortal
• Neutral
• Solid
• Periodic

Example:

• Atom is neutral

NOT BE-compatible adjectives

• Tall (comparative)
• Bigger than X (relational)
• Useful (functional)
• Broken (event-derived)

3. Verbs (Other Than BE) — NOT by BE

Examples:

• Run
• Eat
• Move
• Process
• Heat

These answer:

What does it do?

→ DO, not BE.

4. Other Parts of Speech — NOT by BE

Adverbs

• Quickly, slowly → modify action

Prepositions

• In, on, of, with → relations

Determiners

• A, the, every → scope control

Pronouns

• He, it, which → reference

None define what something is.

Final Classification Rule (Keep This)

BE applies only to:

• Essential nouns (kinds)
• Predicative, non-relational adjectives

No other part of speech is ontologically by BE.

One-Line Anchor

BE is not about grammar.

It is about essence.

This closes the loop between linguistics and ontology precisely.

Classification of Nouns by BE (Ontological Classification)

This classification answers which nouns are legitimately grounded in BE
and which are not, based on essence vs non-essence.

Core Principle

A noun is BE-grounded only if it names what something is by essence.

Grammar allows all nouns.

Ontology accepts only some as BE-classes.

I. Nouns Grounded in BE (Essential / Kind Nouns)

These nouns denote essence, identity, or natural kind.

1. Natural-Kind Nouns

• Human
• Animal
• Mammal
• Electron
• Quark
• Atom

Reason

They answer: What kind of thing is this?

Example:

• Human is an Animal

2. Structural / Formal Nouns

• Triangle
• Crystal
• Molecule
• Atom (as structure)

Reason

Their identity depends on necessary structure.

Example:

• Triangle is a three-sided polygon

3. Constitutive / Material-Kind Nouns

• Water
• Iron
• Silicon
• Protein

Reason

Their constitution is essential, not accidental.

Example:

• Water is H₂O

4. Mathematical / Logical Class Nouns

• Number
• Prime
• Set
• Function

Reason

Defined purely by formal essence.

Example:

• Prime number is divisible only by 1 and itself

5. Biological Species Nouns

• Homo sapiens
• Canis lupus

Reason

Species are classes (universals) whose instances are organisms.

Example:

• Human is Homo sapiens

II. Nouns NOT Grounded in BE (Non-Essential)

These nouns form classes, but not BE-classes.
They are defined by conditions, not identity.

6. Property Nouns (HAS-derived)

• Color
• Height
• Mass
• Charge

Why not BE
They answer what it has, not what it is.

7. Role Nouns

• Student
• Teacher
• Driver
• Patient

Why not BE
Roles are contextual and temporary.

8. Function Nouns (WHY-derived)

• Tool
• Device
• Sensor
• Weapon

Why not BE
Defined by purpose, not essence.

9. Relation Nouns

• Neighbor
• Member
• Owner
• Part

Why not BE
Defined by relation to others.

10. State / Condition Nouns

• Illness
• Charge (as state)
• Motion
• Rest

Why not BE
States are time-bound, not identity.

11. Event / Process Nouns

• Running
• Heating
• Computation
• Collision

Why not BE
Events occur; they are not beings.

Summary Table

Final Rule (Keep This)

BE grounds kinds (what something is).

Other nouns describe qualifications (how it is, what it has, or what it does).

One-Line Anchor

Not every noun names a being;

only essential nouns are BE-nouns.

Part–Whole vs BE Relations (Illustrated Examples)

This section clarifies Particular–Universal and Part–Whole (mereology)
using your three concrete examples.

1. Me (Whole) and My Heart (Organ)

Ontological Status

• Me → particular whole
• My heart → particular part

Correct Relations

• HAS (part-of)
  
• BE (is-a) only for classification

Valid Statements

• I have a heart.
• The heart is an organ.
• The heart is part of me.

Invalid Statements

• ❌ I am my heart.
• ❌ Heart is me.

Key Point:

This is mereology (part–whole), not class membership.

2. Quarks and Atoms

Ontological Status

• Quark → fundamental part
• Atom → composite whole

Correct Relations

• HAS (constitutive part)
• BE only for identity/class

Valid Statements

• An atom has constituents.
• Hadrons have quarks.
• A quark is a fundamental fermion.

Important Note

• Quarks are non-separable parts
• They are real but never standalone wholes

Key Point:

Quark → Atom is a part-only to whole relation.

3. My Particular Neuron and a Particular Cell Part of That Neuron

Note: A neuron itself is a cell; here we refer to its subcellular parts.

Ontological Status

• My neuron → particular whole
• Subcellular part → particular part

Correct Relations

• HAS (part-of) recursively
• BE for classification only

Valid Statements

• My neuron is a neuron.
• My neuron has a soma, axon, and dendrites.
• This axon segment is part of my neuron.

Nested Part–Whole Chain

Me
└── Nervous System
    └── Neuron (particular)
        └── Subcellular parts (particular)

Unified Pattern

Final Ontological Rule

BE connects an entity to its kind.

HAS connects a whole to its parts.

No part–whole relation is ever a BE relation.

Inseparable Parts of a Whole That Are Treated as Classes

Core Idea

Some parts are inseparable from their wholes yet are still treated as classes

because they have a stable identity, properties, and laws of their own.

These are ontologically real parts, not abstractions, and thus qualify as classes (universals).

What “Inseparable but Class-Treated” Means

An inseparable part:

• Cannot exist independently as a whole
• Cannot be isolated in practice or principle
• Exists only as part of a larger whole

Yet it is treated as a class if it:

1. Has a distinct identity
2. Has law-governed properties
3. Recurs across many wholes
4. Can be classified and theorized independently

Canonical Examples

1. Quark (Physics)

• Whole: Hadron (proton, neutron)
• Status: Non-separable constituent
• Why a class:
  • Distinct flavors (up, down, strange, etc.)
  • Fixed quantum numbers
  • Governed by QCD

✔ Treated as a class despite non-separability

2. Electron Cloud / Orbital (Atomic Physics)

• Whole: Atom
• Status: Cannot exist without a nucleus (bound state)
• Why a class:
  • Orbitals (s, p, d, f) are classified
  • Have defined energies and symmetries

✔ Class-level treatment of inseparable structure

3. Gene (Biology)

• Whole: Genome / chromosome
• Status: Cannot function outside cellular context
• Why a class:
  • Defined by structure and function
  • Repeats across organisms

✔ Class even though context-bound

4. Neuron (Biology)

• Whole: Nervous system
• Status: Cannot survive independently
• Why a class:
  • Distinct morphology and function
  • Governed by electrophysiological laws

✔ Inseparable in practice, class in ontology

5. Phoneme (Linguistics)

• Whole: Language system
• Status: No standalone existence
• Why a class:
  • Abstract unit with contrastive identity
  • Repeats across utterances

✔ Abstract but class-level

6. Wave Mode / Normal Mode (Physics)

• Whole: Field or system
• Status: Exists only in the system
• Why a class:
  • Quantized modes recur
  • Obey mathematical laws

✔ Class without separability

What Is NOT Treated as a Class (Even If Inseparable)

❌ Accidental fragments

• A broken shard of glass

❌ Temporary states

• “Being hot”, “being charged”

❌ Context-only relations

• “Left side”, “neighbor”

These lack stable identity across wholes.

Summary Table

Final Rule (Keep This)

An inseparable part is treated as a class

if it has stable identity and explanatory autonomy,

even without independent existence.

One-Line Anchor

Separability is not required for classhood;

identity and lawfulness are.

Classes of Matter (Ontological Classification)

This classification lists matter-classes grounded in BE

(i.e., classes defined by what they are, not by role, function, or state).

The ordering is from most fundamental to most composite.

1. Fundamental Matter Classes (Physics)

1.1 Elementary Matter Particles

(No internal structure in the Standard Model)

• Quarks (up, down, strange, charm, top, bottom)
• Leptons (electron, muon, tau, neutrinos)

✔ Class type: Natural kind

✔ BE-grounded: Yes

✔ Note: Quarks are non-separable, yet real matter classes

2. Composite Subatomic Matter Classes

2.1 Hadrons

(Composite of quarks)

• Baryons (proton, neutron)
• Mesons

✔ Class type: Structural / constitutive

✔ BE-grounded: Yes

2.2 Atomic Constituents

• Nucleus
• Electron cloud (bound electrons)

✔ Class type: Structural

✔ BE-grounded: Yes

3. Atomic Matter Classes

3.1 Atoms

• Hydrogen atom
• Carbon atom
• Iron atom

✔ Class type: Chemical natural kinds

✔ BE-grounded: Yes

4. Molecular Matter Classes

4.1 Molecules

• H₂O
• CO₂
• Proteins
• DNA

✔ Class type: Constitutive / structural

✔ BE-grounded: Yes

5. Ionic Matter Classes

• Cations
• Anions

✔ Class type: Structural charge-defined matter

✔ BE-grounded: Yes

6. Lattice / Network Matter Classes

6.1 Crystalline Matter

• Ionic crystals
• Covalent crystals
• Metallic crystals

6.2 Amorphous Matter

• Glass
• Polymers

✔ Class type: Structural matter kinds

✔ BE-grounded: Yes

7. Phase-Based Matter Classes

(Phase is essential when stable)

• Solid
• Liquid
• Gas
• Plasma

✔ Class type: Physical state classes

✔ BE-grounded: Yes (when stable, not transient)

8. Material Classes (Macroscopic Matter)

• Metals
• Ceramics
• Polymers
• Semiconductors
• Composites

✔ Class type: Material kinds

✔ BE-grounded: Yes

9. Biological Matter Classes

9.1 Cellular Matter

• Prokaryotic cells
• Eukaryotic cells

9.2 Multicellular Matter

• Tissues
• Organs

✔ Class type: Biological natural kinds

✔ BE-grounded: Yes

10. Aggregate Matter Classes

• Granular matter
• Powders
• Foams
• Colloids

✔ Class type: Collective material kinds

✔ BE-grounded: Yes

What Is NOT a Class of Matter (Important)

❌ Energy (not matter)

❌ Force / interaction

❌ Function (tool, device)

❌ State-only descriptors (hot, cold – temporary)

❌ Relations (near, connected)

Summary Table

Final Anchor Statement

A class of matter is defined by what it is,

not by what it does or is used for.

This list is ontology-complete and BE-consistent.

Classes in Biology and Biological Taxonomy

This section clearly distinguishes biological classes grounded in BE (essence)
from organizational taxonomic ranks and non-taxonomic biological groupings.

1. What “Class” Means in Biology (Ontology)

In biology, a class is a universal grounded in biological essence.

Biological essence is defined by:

• common ancestry (evolutionary lineage)
• shared genetic and developmental constraints
• stable reproductive continuity

Thus, biological classes are natural kinds, not arbitrary groupings.

2. Biological Taxonomy (Linnaean System)

All taxonomic ranks denote classes (universals).
They differ only in generality, not in ontological status.

Standard Taxonomic Hierarchy

Domain
└── Kingdom
    └── Phylum
        └── Subphylum
            └── Class
                └── Order
                    └── Family
                        └── Genus
                            └── Species

3. Ontological Status of Each Rank

Individuals appear only below species.

4. Species as a Class (Critical Clarification)

• Species is not an individual
• Species is a class whose instances are organisms

Example:

• Prasanth → particular organism
  
• Homo sapiens → biological class

Logical form:

Homo_sapiens(x)

5. BE-Relations in Biological Taxonomy

All taxonomic relations are BE (is-a) relations.

Examples:

• Human is a Mammal
  
• Mammal is an Animal
  
• Animal is a Living Being
  

No taxonomic relation is part–whole.

6. Biological Classes Outside Formal Taxonomy

Some biological classes are real but non-Linnaean.

Still BE-grounded

• Cell
• Neuron
• Tissue
• Organ
• Protein
• Gene

These are:

• biological natural kinds
• grounded in structure and function essential to life

7. What Are NOT Biological Classes (Not BE-grounded)

These are biological groupings, not essential classes.

❌ Role-based

• Predator
• Pollinator
• Host

❌ State-based

• Diseased cell
• Dormant seed

❌ Function-based

• Signal molecule
• Transport protein (functional label only)

❌ Relation-based

• Symbiont
• Neighboring species

These do not define what the entity is.

8. Summary Table

Final Rule (Keep This)

In biology, classes are defined by lineage and necessity,

not by role, state, or ecological function.

One-Line Anchor

Biological taxonomy is a hierarchy of BE-grounded classes

whose instances are living organisms.

Matter Taxonomy by BE (Is-a Only)

This taxonomy classifies matter strictly by BE (what it is).
No part–whole, no function, no biological reinterpretation.

Matter
└── Fundamental
    ├── Fermionic
    │   ├── Quark
    │   └── Lepton
    └── Composite Subatomic
        └── Hadronic
            ├── Baryonic
            └── Mesonic

└── Atomic
    ├── Element
    │   ├── Metal
    │   ├── Non-metal
    │   ├── Metalloid
    │   └── Noble Gas
    └── Atom

└── Ionic
    ├── Cation
    └── Anion

└── Molecular
    ├── Molecule
    ├── Compound
    ├── Simple Molecular Substance
    ├── Supramolecular
    └── Macromolecule

└── Structural
    ├── Crystalline
    │   ├── Ionic Crystal
    │   ├── Covalent Crystal
    │   └── Metallic Crystal
    ├── Amorphous
    └── Microstructured

└── Phase
    ├── Solid
    ├── Liquid
    ├── Gas
    └── Plasma

└── Material
    ├── Metallic Material
    ├── Ceramic Material
    ├── Polymeric Material
    ├── Semiconducting Material
    └── Composite Material

└── Cellular
    └── Cell

└── Multicellular
    ├── Tissue
    ├── Organ
    └── Organism

└── Aggregate
    ├── Granular
    ├── Powder
    ├── Foam
    └── Colloid

Why this is correct by BE

Every node answers “What is it?”

Every edge is is-a (BE), not part-of

Molecule and Cell are explicit classes

Biology appears after matter, not redefining it

No function, role, or purpose is introduced

Key clarification (important)

Cell is matter → organized matter

Molecule is matter → bonded matter

Biology does not replace matter taxonomy

It specializes it later (not shown here)

Anchor rule (keep this)

Matter taxonomy by BE must include Molecule and Cell explicitly.
Any taxonomy that skips them is incomplete.

This version is ontologically clean, exam-safe, and internally consistent.