ALayer 1A
Axiswhat kind of claim
The kind of truth at stake — veridical, authenticity, sincerity, normative, essence, verification.
6 primary · 4 meta
The Machinery
The Semantic Constraint Architecture
AOML v2.2 — Axis · Operator · Method · Level. The reference the rest of the series is built on: the axes a claim can live on, the operators that compose them, the methods that validate them, the levels they occupy — and the legality matrix that says what may combine with what.
A · O · M · L
Every claim carries a coordinate.
Four dimensions locate any truth-claim. Get the coordinate right and the claim is well-formed; cross a boundary the matrix forbids and you have one of the five violation types.
OLayer 1C
Operatorwhat transformation
The structural move asserted on an axis — attribute, cause, become, result, abstract, stratify, contrast, reveal.
8 operators
MHabitat
Methodwhat validates it
The validation habitat proper to the claim — observation, provenance, testimony, logic, and the rest.
8 methods
LLayer 1D
Levelwhat stratum
The level of abstraction it operates at — empirical, conventional, formal, ultimate.
4 levels
The Legality Matrix
What each axis lets each operator do.
Six primary axes down, eight operators across. Each cell records whether the composition is licensed, restricted, or blocked — plus the one universal block attested in all sixteen languages. Select a cell for the condition behind it.
✓ Licensed△ Restricted✗ Blocked✗ Universal block
| axis · operator | ATTR | CAUSE | BECOME | RESULT | ABSTR | STRAT | CONTR | REVEAL |
|---|---|---|---|---|---|---|---|---|
| VEREpistemic | ||||||||
| VERIFEpistemic | ||||||||
| AUTHOntological | ||||||||
| ESSOntological | ||||||||
| SINCDispositional | ||||||||
| NORMInstitutional |
Select any cell to read the condition that governs it.
Axes
The kinds of truth.
Six primary axes — what kind of claim is being made — and four meta-axes that modulate a primary claim without ever standing in for it.
| Code | Axis | What it covers | Class |
|---|---|---|---|
| VER | Veridical | Is it so in the world? Factual correspondence between claim and state of affairs. | Epistemic |
| AUTH | Authenticity | Genuine or counterfeit? Origin integrity — settled by provenance, not appearance. | Ontological |
| SINC | Sincerity | Honestly meant? Alignment between stated and actual belief; read from conduct. | Dispositional |
| NORM | Normative | Right or just? Ought-claims, validated by principle or consensus. | Institutional |
| ESS | Essence | What is it by nature? Definitional, necessary properties. | Ontological |
| VERIF | Verification | Has it been proven? The epistemic act of establishing a claim. | Epistemic |
Meta-axes — the M[A] ↛ A family
| Code | Meta-axis | Modulation | Rule |
|---|---|---|---|
| DEG | Degree | Magnitude — intensity, threshold, comparison. The derivative of the claim. | R5 |
| TEMP | Temporal | Position in time — order, persistence; its internal level-crossing is Type 4. | R6 |
| LIKE | Likeness | “Resembles A without being A” — forgery, hypocrisy, sophistry, truthiness. | R8 |
| EVID | Evidentiality | Source-marking — witnessed, reported, or inferred. | R9 |
R5, R6, R8, R9 are one schema — M[A] ↛ A: a modulated claim never discharges into the claim. All four are Operator Overextension (Type 2).
Operators
The moves you can make on an axis.
| Code | Operator | Meaning |
|---|---|---|
| ATTR | Attribution | “X is [axis].” The basic assertion — licensed on every axis. |
| CAUSE | Causation | “Make X [axis].” An external agent produces the state — the most restricted operator. |
| BECOME | Becoming | “X becomes [axis].” A transition into the state; directionally biased. |
| RESULT | Result | “X turned out to be [axis].” An achieved or discovered state. |
| ABSTR | Abstraction | “Truth,” “justice.” Nominalizes an axis-property into a standalone concept. |
| STRAT | Stratification | “Surface vs. deep [axis].” Marks internal contrast within an axis. |
| CONTR | Contrast | “Not true,” “invalid.” Predicates the negative pole — universal across languages. |
| REVEAL | Revelation | “X was revealed to be [axis].” Discloses a latent, pre-existing state. |
Validation Habitats
Each axis has a method that fits it.
Use the wrong instrument for the kind of claim and you commit a Type 3 Verification Habitat Mismatch.
| Axis | Default method | Inadmissible | Type-3 example |
|---|---|---|---|
| VER | Observation, experiment | Consensus, testimony, principle | Appeal to authority; bandwagon |
| AUTH | Provenance | Consensus, appearance alone | Argument from appearance |
| SINC | Testimony & conduct over time | Experiment, single-instance observation | Passion as evidence |
| NORM | Principle, consensus | Observation, experiment | Naturalistic fallacy; is–ought |
| ESS | Logic | Observation, consensus, statistics | No true Scotsman; definitional fallacy |
| VERIF | Experiment, statistics, logic | Testimony alone, consensus | Ipse dixit; verification by consensus |
Levels
And the stratum it operates at.
Crossing a level boundary without a warrant is a Type 4 Stratification Failure.
| Code | Level | Validated by | Default for |
|---|---|---|---|
| EMP | Empirical | Observation, experiment | VER, AUTH |
| CONV | Conventional | Consensus, principle | SINC, NORM |
| FORM | Formal | Logic, statistics | ESS, VERIF |
| ULT | Ultimate | Definitional necessity | ESS often reaches here |
Structural Rules
The nine empirical constraints, R1–R9.
Each is a boundary the sixteen-language evidence draws on the matrix; every one resolves to a violation type.
| # | Name | Statement | Type |
|---|---|---|---|
| R1 | Dispositional Causation Block | CAUSE × SINC universally blocked (16/16 languages) | 2 |
| R2 | Essence Stability | CAUSE × ESS, BECOME × ESS blocked | 2 |
| R3 | Authenticity Polarity | CAUSE+ × AUTH blocked; CAUSE− licensed | 2 |
| R4 | Positive Emergence Bias | BECOME(+) ≫ BECOME(−) across truth-domain axes | 2 |
| R5 | Degree Substitution | DEG[A] ↛ A in any inference step | 2 |
| R6 | Temporal Substitution | TEMP[A] ↛ A; internal level-crossing → Type 4 | 2 / 4 |
| R7 | Agentive Polarity | Agentive ABSTR+ blocked, − licensed (“liar” lexicalizes; “truth-teller” does not) | 2 |
| R8 | Likeness Substitution | LIKE[A] ↛ A in any inference step | 2 |
| R9 | Evidentiality Substitution | EVID[A] ↛ A in any inference step | 2 |
This page is a working overview. The full v2.2 specification — every condition, the empirical basis across sixteen languages, and the machine-readable matrix — lives in the deposit.