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pr4xis
Axiomatic intelligence.
Doing the right thing — with proof.
“Every good regulator of a system must be a model of that system.” — Conant & Ashby (1970)
What is pr4xis?
Aristotle named three kinds of knowing:
- episteme — knowing how things ARE (science)
- techne — knowing how to MAKE things (technology)
- praxis — the doing itself, done well
pr4xis is the doing.
Domain knowledge lives in composable ontologies. Not in mechanical processing logic. No parser-with-special-cases, no rules with hardcoded strings. Every transformation is a proven functor. Every claim traces to an axiom.
How it works
Define rules (Ontology) → Check rules (Engine) → Prove rules hold (Tests)
↑ |
└──────────── feedback ────────────────────────┘
The ontology IS the model. The engine IS a control system.
Conant-Ashby (1970) proven in code: Model → Ontology.
The Architecture
| Layer | What it does |
|---|---|
| Logic | Axioms, propositions, inference |
| Category | Entities, relationships, composition, functors |
| Ontology | Domain knowledge, reasoning patterns, DOLCE |
| Engine | Situations, actions, preconditions, enforcement |
| Codegen | Declarative ontology delivery — build-time, async runtime, mmap (proven equivalent as functors) |
No domain logic in framework code. Adding chess, physics, or English changes nothing in the engine.
Domains compose via functors
If Chess IS EventDriven (functor) and EventDriven IS Concurrent (functor), then Chess IS Concurrent (composition). The proof is automatic.
| Functor | Proof |
|---|---|
| Traffic → Systems | Identity + composition preserved |
| Chess → EventDriven | Identity + composition preserved |
| Chess → Concurrent | Composed from above |
| Dialogue → Communication | Identity + composition preserved |
| Control → Engine | Plant→Situation, Model→Ontology |
| Lambek → Pregroup | Parsing preserved across type systems |
Natural Language Pipeline
Text → Language::lexical_lookup → Pregroup types → Contract → Semantics → Response
- Language trait — language-agnostic. English, Hebrew, same code.
- Pregroup grammar — parsing as group algebra (Lambek 1999)
- Montague functor — syntax → semantics (proven)
- Zero hardcoded words — everything through the ontology
np · n^l · n · np^r · s → contract → s — “the dog runs” parsed by algebra.
Turing Test Benchmark
Questions from real competitions (Loebner Prize, Winograd Schema Challenge).
| Level | Status | What’s needed |
|---|---|---|
| Taxonomy (“is a dog a mammal?”) | 3 PASS | WordNet (107K concepts) |
| Grammar (“the dog runs”) | 2 PENDING | Pregroup pipeline |
| Factual (“capital of France?”) | 3 PENDING | Geography, Literature, Mereology |
| Reasoning (“brick weight puzzle”) | 2 PENDING | Arithmetic ontology |
| Winograd (“trophy too big”) | 3 PENDING | Physical world + DRT |
| Common sense (“drop an egg?”) | 2 PENDING | Material/sensation ontology |
| Social (“how are you?”) | 1 PENDING | Social dialogue ontology |
| Meta (“are you a computer?”) | 2 PENDING | Self-model + metacognition |
Every pending test = a research task. When the ontology is built, the test passes.
pr4xis vs LLMs
| LLMs | pr4xis | |
|---|---|---|
| How it knows | Learned from training data | Derived from accepted axioms |
| Correctness | Approximate — best guess from patterns | Checked — every claim verified against its axioms |
| Hallucination | Inherent — no ground truth | Every claim traces to a proof; where the axioms don’t reach, it abstains |
| Determinism | Stochastic | Deterministic — same input, same derivation |
| Traceability | Opaque weights | Full proof path back to axioms |
| When wrong | Confidently wrong, hard to find why | The failing axiom is named |
| Cross-domain reasoning | Implicit blending | Proven connections between domains |
| Missing knowledge | Doesn’t know what it doesn’t know | Detects gaps automatically |
Contributions
pr4xis architecture — a synthesis built on a sixty-year intellectual lineage:
- Domain knowledge in composable ontologies — every domain is a category in the formal sense (Guarino 1998 framing; Spivak ologs as prior art)
- Functorial composition between behavioral ontologies — extending Spivak’s data-migration pattern from schemas to behavior
- Conant-Ashby as architectural justification — the engine is a model because the theorem requires it
- DOLCE as upper layer with category theory as the substrate — both used together
- Composable proof chains — if A IS B and B IS C, then A IS C, by functor composition
Academic Foundation
50+ papers, all downloaded and cited:
- Category theory — Mac Lane, Awodey, Spivak (ologs)
- Control systems — Wiener, Ashby, Conant-Ashby, Powers
- Formal ontology — DOLCE, Guarino, Gangemi (ODPs)
- Linguistics — Lambek, Montague, Kamp (DRT), Steedman (CCG)
- Information — Shannon, Damerau, Brill & Moore
- Metacognition — von Foerster, Spencer-Brown
Full lineage: docs/understand/foundations.md
Live Demo
~107,000 WordNet concepts. Running in your browser right now. No server, no GPU, no API key.
What’s next
- More ontologies — each grammar gap and missing concept is a research task
- More functors — importing BioPortal, the Gene Ontology, OBO Foundry, DOLCE as composable categories
- Hebrew — a second language proves the architecture is language-agnostic
- Drafts in flight — three research papers on bioelectricity, gap detection, and ontology diagnostics; see
docs/research/papers/
The name pr4xis is not marketing. It is a claim backed by cargo test --workspace.
Thank you
Axiomatic intelligence. Domain knowledge in composable ontologies. Every claim has a proof.