PLCI v1.1 — Extended Propositional Logic Conversion Instrument

A Formal, Enforceable System for Converting Natural Language into Structured Logical Form

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I. Governing Principle

A text must be factored into a layered logical system.
Flattened outputs are invalid.

All outputs must satisfy:

• structural separation
• explicit inference
• modal clarity
• temporal clarity
• bounded interpretation

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II. Logical Layers (Mandatory Taxonomy)

Every proposition must be assigned to exactly one primary layer:

1. Ontological (Oₙ) — what exists / what something is
2. Axiological (Aₓ) — what is good, bad, indifferent
3. Epistemic (Eₚ) — belief, judgment, knowledge, error
4. Causal (Cₐ) — what produces or prevents
5. Psychological (Pₛ) — fear, desire, disturbance, impulse
6. Normative (Nₒ) — obligation, prohibition, permission
7. Practical (Pᵣ) — action directives
8. Social/Relational (Sᵣ) — roles, authority, relations
9. Modal (Mₒ) — necessity, possibility
10. Temporal (Tₑ) — persistence, timing
11. Inferential (Iₙ) — logical dependencies

Rule L1 (Layer Integrity):
No proposition may belong to more than one layer.

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III. Symbol System

Core Logic

• ¬P — not P
• P ∧ Q — and
• P ∨ Q — or
• P → Q — if P then Q
• P ↔ Q — iff

Quantifiers

• ∀x — for all
• ∃x — exists

Deontic

• O(P) — obligatory
• F(P) — forbidden
• Perm(P) — permitted

Modal

• □P — necessarily P
• ◇P — possibly P

Temporal

• Always(P)
• Sometimes(P)
• At(t, P)

Causal

• Causes(P, Q)

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IV. Atomic Extraction Protocol (AEP)

Definition

A proposition is atomic if:

1. It contains one predicate assertion
2. It cannot be split without introducing a logical operator

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Rule A1 (Forced Decomposition)

If a sentence contains:

• and
• because
• if
• therefore
• unless

→ it must be split into multiple propositions.

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Rule A2 (Minimality)

Each proposition must express exactly one claim.

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V. Conversion Procedure

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Step 1 — Subject Definition

State:

• the domain
• the central problem

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Step 2 — Predicate Key

Define all symbols before use.

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Step 3 — Atomic Extraction

Apply AEP strictly.

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Step 4 — Layer Assignment

Assign each proposition to one layer.

Violation → invalid output.

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Step 5 — Formalization

Translate into symbolic or semi-symbolic form.

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Step 6 — Hidden Premise Protocol

Rule HP1 (No Silent Inference)

Every inferential jump must include:

• explicit premise, or
• HPx (hidden premise)

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Rule HP2 (Minimality)

Hidden premises must be:

• necessary
• non-redundant

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Step 7 — Causal vs Logical Distinction

Rule C1

• If X produces Y → Causes(X, Y)
• If X entails Y → X → Y

Never conflate.

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Step 8 — Deontic Encoding

Rule D1

All normative language must use:

• O(P), F(P), or Perm(P)

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Rule D2

Every obligation must have grounding.

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Step 9 — Modal Encoding

Rule M1

If the text expresses:

• necessity → □P
• possibility → ◇P

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Step 10 — Temporal Encoding

Rule T1

If the text implies:

• persistence → Always(P)
• recurrence → Sometimes(P)
• timing → At(t, P)

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Step 11 — Inferential Construction

Every system must include explicit derivations.

Rule I1 (Inference Tagging)

Each inference must be labeled:

• T — textual
• D — derived
• A — assumed

Example:

I1 (D): [P1 ∧ P2] → P3
I2 (A): [P3 ∧ HP1] → P4

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Step 12 — Error Condition Layer

Rule E1

Define at least one:

• Error condition
• Failure condition

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Rule E2

Failure must be internally grounded unless text states otherwise.

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Step 13 — Boundary Enforcement

Rule B1

A proposition is valid only if:

• explicitly stated
• logically entailed
• minimally required as HP

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VI. Output Structure (Mandatory)

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1. Subject and Scope

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2. Predicate Key

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3. Layered Propositions

Oₙ — Ontological

Aₓ — Axiological

Eₚ — Epistemic

Cₐ — Causal

Pₛ — Psychological

Nₒ — Normative

Pᵣ — Practical

Sᵣ — Social

Mₒ — Modal

Tₑ — Temporal

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4. Hidden Premises

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5. Inferential Chain (Tagged)

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6. Error Conditions

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7. Compressed Logical Core

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8. System Classification

Select one:

• Argument
• Diagnostic system
• Normative system
• Mixed system
• Metaphysical system

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VII. Audit Protocol

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Audit 1 — Structural

• All propositions layered?
• No mixing of layers?

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Audit 2 — Logical

• All inferences justified?
• Hidden premises identified?

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Audit 3 — Modal/Temporal

• Necessity encoded?
• Time encoded?

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Audit 4 — Boundary

• Any unjustified additions? → remove

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VIII. Failure Modes

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FM1 — Flattening

Loss of structure

FM2 — Normative Collapse

Treating “ought” as “is”

FM3 — Causal Confusion

Mixing causation and implication

FM4 — Hidden Premise Omission

FM5 — Modal Blindness

FM6 — Temporal Blindness

FM7 — Over-Interpretation

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IX. Minimal Execution Form

1. Define subject
2. Extract atomic claims
3. Assign layers
4. Formalize
5. Add hidden premises
6. Build inference chain
7. Encode modality/time
8. Define error conditions
9. Compress

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X. Activation Directive

Use:

Apply PLCI v1.1. Factor the text into layered propositions. Enforce atomic extraction. Separate causation from implication. Encode normativity, modality, and temporality. Identify hidden premises. Tag all inferences. Enforce boundary rules. Produce compressed logical core.

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XI. Final Status

PLCI v1.1 is now:

• enforceable
• auditable
• layer-complete
• modal-temporal aware
• Sterling-compatible

It is no longer a formatting tool.

It is a logic engine for textual systems.