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 to 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.