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Domain Catalog

Note (2026-07-11): This page is in transition. The previous catalog enumerated ~21 domains using a science::math / games::chess / systems::* organization that no longer matches the codebase. The current workspace contains 182 ontologies under a different structure (formal/applied/social/natural/cognitive), and a hand-maintained catalog of every entry is not the right shape going forward. Instead, this page now points at the canonical source, the current organization, and the two pieces of in-flight work that will replace it: per-ontology READMEs (#57) and the source-of-truth report pipeline (#60).

Canonical source

Every ontology lives at exactly one path under crates/domains/src/. The full list is re-derivable by:

find crates/domains/src -name ontology.rs

Pipe it to | wc -l to count; today that returns 182 ontologies.

Every ontology directory contains an ontology.rs file with the pr4xis::ontology! invocation that declares its concepts, kinded morphisms, axioms, and metadata. To understand any specific ontology, read its ontology.rs directly. Per-ontology README.md and citings.md files are pending #57.

Current organization

crates/domains/src/
├── formal/                      formal sciences — math, information, calculator, meta
│   ├── math/                    linear algebra, geometry, probability, statistics, signal
│   │                            processing, control theory, rotation, temporal, quantity
│   ├── information/             communication, concurrency, dialogue, events, knowledge,
│   │                            measurement, provenance, schema, storage, systems, diagnostics
│   ├── calculator/              scientific calculator with exact rationals
│   └── meta/                    ontology diagnostics, gap analysis, archive,
│                                knowledge-graph, artifact-identity,
│                                well-behaved-lens, source-taxonomy
│
├── applied/                     applied engineering domains
│   ├── sensor_fusion/           Kalman filter, observation, state, time, frame, fusion
│   ├── navigation/              AHRS, GNSS, IMU, INS-GNSS, celestial, odometry
│   ├── perception/              occupancy grid, lidar-camera, radar-camera fusion
│   ├── tracking/                single-target, multi-target, radar tracking
│   ├── space/                   orbital mechanics, attitude determination
│   ├── underwater/              sonar, AUV control
│   ├── industrial/              process, structural engineering
│   ├── localization/            SLAM, terrain
│   ├── hardware/                elevator dispatch, traffic signal control
│   └── theming/                 base16 color theme validation, WCAG contrast
│
├── social/                      social and human-system domains
│   ├── games/                   chess, rubik, tetris, simon
│   ├── software/                HTTP state machine, XML, OWL, RDF, LMF
│   ├── judicial/                case lifecycle, motion workflow, evidence, burden of proof
│   ├── compliance/              escalation ladder
│   └── military/                electronic warfare, situation awareness
│
├── natural/                     natural sciences
│   ├── physics/                 kinematics, relativity, energy
│   ├── biomedical/              biology, molecular, bioelectricity, biochemistry,
│   │                            biophysics, mechanobiology, immunology, pharmacology,
│   │                            pathology, hematology, electrophysiology, regeneration,
│   │                            chemistry, acoustics
│   ├── hearing/                 acoustics, anatomy, audiology, neuroscience, psychoacoustics,
│   │                            transduction, vestibular, music perception, signal processing,
│   │                            speech, environmental, devices, pathology, bone conduction
│   ├── geodesy/                 coordinate systems, reference frames
│   ├── colors/                  RGB, WCAG contrast, color theory
│   ├── physics/                 mechanics, electromagnetism, energy
│   └── music/                   scales, chords, intervals
│
└── cognitive/                   cognitive and linguistic domains
    ├── linguistics/             english (WordNet), grammar, lambek pregroup, lexicon,
    │                            morphology, orthography, pragmatics, semantics, symbols
    └── cognition/               epistemics, metacognition, self-model

This tree is the schematic view; it is not exhaustive (some sub-modules are omitted for brevity). For the complete list of every ontology directory, run find crates/domains/src -name ontology.rs.

Cross-domain functors

Domains are not isolated. They compose through proven functors — structure-preserving maps whose laws are checked at test time. To count the functor implementations in the workspace, run:

grep -rn "impl Functor" crates/domains/src/ crates/pr4xis/src/ | wc -l

The most distinctive use of the functor machinery is in the biomedical stack, where three categorical adjunctions (Molecular ⊣ Bioelectric, Biology ⊣ Bioelectric, Pharmacology ⊣ Molecular) automatically detect missing distinctions in the source ontologies. To see the live percentages of how much information is lost in each round-trip:

cargo test -p pr4xis-domains test_full_chain_collapse_measurement -- --nocapture

For the explanation of what these numbers mean, see the README and Concepts.

Why this page is short

A domain catalog written by hand goes stale immediately. Every commit that adds, removes, or renames an ontology silently invalidates a hand-maintained list. The right shape for this page is automated generation from the codebase, plus per-ontology pages for depth. Both are in flight:

  • #57 — every ontology directory gets a README.md (one paragraph: what it models, its scope, its functor connections, its status) and a citings.md (the ontology’s bibliography). The README is the abstract, citings.md is the bibliography.
  • #59 — every per-ontology README also gets two mermaid diagrams: an internal structure view (concepts and relations) and an external connections view (functors and adjunctions to other ontologies). Auto-generated from Concept::variants() and the existing functor implementations.
  • #60 — a CI-generated pr4xis-report.json that captures every numerical metric the codebase produces (test counts, ontology counts, functor counts, adjunction collapse percentages, per-ontology entity/relation counts) and publishes it to GitHub Pages so the README and this catalog can pull live numbers instead of hand-typing them.

When all three land, this page becomes either a redirect to a generated catalog or a thin wrapper around the live JSON.

  • Document date: 2026-04-14
  • Verification: the ontology count and functor count above are re-derivable by the cited find and grep commands. The structural tree is hand-typed and may drift; the canonical source of truth is crates/domains/src/ itself.