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)

Logger
i-am-logger

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:

  1. Domain knowledge in composable ontologies — every domain is a category in the formal sense (Guarino 1998 framing; Spivak ologs as prior art)
  2. Functorial composition between behavioral ontologies — extending Spivak's data-migration pattern from schemas to behavior
  3. Conant-Ashby as architectural justification — the engine is a model because the theorem requires it
  4. DOLCE as upper layer with category theory as the substrate — both used together
  5. 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

Logger
i-am-logger

github.com/i-am-logger/pr4xis

Axiomatic intelligence. Domain knowledge in composable ontologies. Every claim has a proof.