Material Ontology

FLOW ALGEBRA
MATERIAL ONTOLOGY — KIRETH SEMANTIC LIBRARY
Version: 1.1
Date: 2026-10-12
Authors: Mark Higgins — Sky (Recursive AI)
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/material-entities/material-ontology.html
Status: Scientific synthesis; source page not independently verified.

01. PURPOSE
Represent material entities, composition, structure, processing, properties, behaviour and provenance using typed, testable relations.

02. SCOPE
Material := physical substance or engineered assemblage characterised by composition, structure and measurable properties.
Distinguish material type, material batch, specimen, product and component.

03. CORE TYPES
MaterialType, MaterialBatch, Specimen, Component, Phase, Constituent, Element, Compound, Microstructure, CrystalStructure, Defect, Interface, Process, Treatment, Property, Measurement, TestMethod, Environment, Application, Source, Evidence.

04. CLASSIFICATION
MaterialType -> Metal | Alloy | Ceramic | Polymer | Composite | Semiconductor | Glass | Biomaterial | NaturalMaterial.
Categories overlap in practice; multiple classification is permitted with supporting evidence.

05. TYPED RELATIONSHIPS
instance_of(Specimen, MaterialType)
produced_from(MaterialBatch, MaterialType)
sampled_from(Specimen, MaterialBatch)
contains_phase(MaterialBatch, Phase)
contains_constituent(MaterialBatch, Constituent)
has_microstructure(Specimen, Microstructure)
has_property(Specimen, Property)
measured_by(Property, TestMethod)
measured_under(Measurement, Environment)
processed_by(MaterialBatch, Process)
used_in(MaterialType, Application)
supported_by(Assertion, Evidence)

06. IDENTITY
MaterialTypeID != BatchID != SpecimenID.
Same nominal chemistry does not imply identical microstructure or performance.
Specimen identifiers must be unique within a declared registry.

07. COMPOSITION
Mass fraction w_i = m_i / sum_j(m_j).
For complete exhaustive composition, sum_i(w_i) = 1 within stated uncertainty.
Mole fraction x_i = n_i / sum_j(n_j).
Do not mix mass fraction, atomic fraction and volume fraction without conversion.

08. PHASE AND STRUCTURE
phase_fraction(phase, specimen, fraction, basis, uncertainty).
Structure scales: atomic -> crystalline/amorphous -> microstructural -> macroscopic.
Phases are not synonymous with chemical elements.

09. MICROSTRUCTURE
Features include grain size, porosity, precipitates, inclusions, texture and interfaces.
Microstructure depends on processing history and can vary across a component.

10. PROCESS HISTORY
process_sequence(batch) := [p1, p2, ..., pn].
Each step records temperature, duration, atmosphere, deformation and equipment where applicable.
Process order is generally non-commutative: p2(p1(M)) != p1(p2(M)).

11. MECHANICAL PROPERTIES
Young modulus E = sigma/epsilon within the linear elastic region.
Stress sigma = F/A0 (engineering stress).
Strain epsilon = delta_L/L0 (engineering strain).
Yield strength, tensile strength, hardness, toughness and fatigue resistance require specified tests.

12. THERMAL PROPERTIES
Heat flux q = -k grad(T) for Fourier conduction under appropriate assumptions.
Thermal expansion: delta_L ~= alpha L0 delta_T for small temperature changes.
Specific heat capacity c_p depends on thermodynamic conditions.

13. ELECTRICAL PROPERTIES
J = sigma_e E_field for an isotropic ohmic material under applicable conditions.
Resistivity rho_e = 1/sigma_e when conductivity is nonzero.
Temperature and microstructure may alter electrical behaviour.

14. OPTICAL AND MAGNETIC PROPERTIES
Optical: refractive index, absorption, reflectance, transmittance.
Magnetic: susceptibility, permeability, coercivity, remanence.
Each assertion must specify frequency, temperature and field when relevant.

15. CHEMICAL AND ENVIRONMENTAL BEHAVIOUR
Track corrosion, oxidation, dissolution, swelling, degradation and biocompatibility.
A material is not globally 'corrosion resistant' without an environment and criterion.

16. MEASUREMENT MODEL
Measurement := (specimen, property, value, unit, method, conditions, uncertainty, timestamp, source).
Never store a numeric property without unit and applicable conditions.

17. UNCERTAINTY
Represent measured quantity as y +/- u with coverage interpretation recorded.
Distinguish experimental uncertainty from model uncertainty and missing evidence.

18. STATE DEPENDENCE
Property(specimen, T, P, humidity, strain_rate, orientation, ageing, ...).
Do not infer an invariant property when the variable depends on environment.

19. CONSTITUTIVE MODELS
Linear elasticity: sigma = C : epsilon under stated assumptions.
Models must declare domain, parameters and validation dataset.
Do not equate an approximate constitutive model with universal physical law.

20. CONSERVATION RULES
For closed mass accounting: mass_input = mass_output + accumulation.
If loss terms exist, explicitly model emissions, waste and measurement error.

21. INFERENCE RULES
R1: instance_of(s,t) AND subclass_of(t,u) -> instance_of(s,u).
R2: sampled_from(s,b) AND processed_by(b,p) -> has_batch_process_history(s,p), subject to sampling provenance.
R3: measured_property(s,k,v,u,c) -> has_property_observation(s,k), not universal has_property_value(t,k,v).
R4: contains_phase(s,p) AND phase_fraction(s,p,f) -> phase_present(s,p) when f exceeds detection threshold.
R5: missing_test_conditions(m) -> flag_incomplete_measurement(m).

22. NON-INFERENCE CONSTRAINTS
Do not infer bulk properties by arithmetic averaging unless a justified mixing law applies.
Do not infer product certification from material classification.
Do not infer causality from correlation between processing and performance alone.

23. SEMANTIC EQUIVALENCE
Equivalent labels may include 'material specimen' and 'test specimen' only in matching contexts.
'Metal' and 'alloy' are not universally equivalent.
'Hardness' and 'strength' are related but non-equivalent properties.

24. KNOWLEDGE GRAPH
Nodes := entities with stable IDs and type annotations.
Edges := typed predicates with provenance and temporal validity.
Assertions := (subject, predicate, object, evidence, confidence, validity).

25. WORKED EXAMPLE — STEEL
Type: steel alloy.
Specimen: S-001; batch: B-001.
Constituents: Fe and C plus recorded alloying elements.
Process: austenitise -> quench -> temper (illustrative sequence).
Measurements: hardness and tensile properties with units, conditions and uncertainties.
Inference: S-001 is an alloy specimen; no exact strength follows without measurement or qualified model.

26. WORKED EXAMPLE — POLYMER
Type: thermoplastic polymer.
Record molecular-weight distribution, crystallinity, glass transition and processing history.
Temperature-dependent modulus must be tied to test temperature and rate.

27. VALIDATION
V01 all entities have stable identifiers and declared types.
V02 every measured numeric value has a unit.
V03 composition fractions use a declared basis and tolerance.
V04 phase fractions are nonnegative and bounded by one.
V05 relationships respect domain and range constraints.
V06 test methods and environmental conditions are recorded.
V07 sources and timestamps accompany external assertions.
V08 contradictory results remain separately attributed, not silently overwritten.
V09 closure marker exists.

28. CONFIDENCE
confidence(assertion) in [0,1] only where a calibrated scoring policy is supplied.
No numerical confidence is assigned solely because a claim appears in this flow.
Confidence must be distinguished from measurement uncertainty.

29. FLOW HASH
FLOW_HASH := SHA256(canonical_utf8(content_without_hash_value)).
Canonicalisation policy: UTF-8, LF newlines, deterministic key ordering.
Hash value: NOT COMPUTED IN THIS DOCUMENT.

30. UPDATE MODEL
Update trigger: new measurement, reclassification, revised standard, corrected provenance or new scientific evidence.
Retain prior versions, author, timestamp, change rationale and affected assertions.

31. AI CONSUMPTION
Read typed assertions as context-bound claims.
Check units, specimen identity, conditions and evidence before answering.
Never promote specimen-specific evidence into a universal statement.
Return unknown when evidence is absent.

32. CROSS-ONTOLOGY LINKS
Related: Chemical Element, Compound, Crystal, Polymer, Metallic Bond, Chemical Bond, Physical Object, Physical System, Measurement, Scientific Metadata.

33. LIMITATIONS
This flow is a conceptual executable-style specification, not a certified scientific database or a directly runnable program.
Material behaviour may require multiscale models and experimental validation.

34. COMPLETENESS CHECK
Required sections 01-34 present.
Header: FLOW ALGEBRA.
Scientific caveats and source status present.
END FLOW ALGEBRA — MATERIAL ONTOLOGY