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BooleanDomain — Semantic Specification

1. Definition

A BooleanDomain is a ValueDomain whose admissible values represent binary truth values.

It defines admissibility strictly as logical truth or falsity.

2. Declaration

A BooleanDomain exists as a specialization that:

  • Admits exactly two logical values
  • Applies strict boolean semantics
  • Rejects all non-boolean inputs

Minimal declaration requirements:

  • Explicit definition of truth and falsity values

No numeric, probabilistic, or categorical interpretation is implied.

3. Semantic Invariants

B1: Binary Exclusivity

Exactly two values are admissible.

B2: Boolean Identity

Admissible values MUST be logically true or false.

B3: No Coercion

Non-boolean values MUST NOT be coerced.

B4: Stability

Truth semantics MUST remain invariant.

4. Negative Definition

What BooleanDomain is NOT.

  • Not numeric
  • Not categorical
  • Not probabilistic
  • Not ternary or fuzzy logic
  • Not extensible

5. Impossibilities

  • A third truth value cannot exist
  • Numeric or string equivalents cannot be accepted
  • Boolean semantics cannot change

6. Boundary Conditions

  • Truth constants: Only canonical boolean values are admissible.

  • Degenerate cases: None permitted.

7. Composition Rules

Allowed

  • BooleanDomain ∘ Variable
  • CompositeDomain(BooleanDomain, …)

Forbidden

  • BooleanDomain ∘ NumericDomain
  • BooleanDomain ∘ CategoricalDomain

8. Example (Non-Normative)

validate(True)  → admissible
validate(False) → admissible
validate(1)     → inadmissible

9. Validation Rules

  • Static: BooleanDomain is valid by construction.

  • Runtime: Any non-boolean value is invalid.

10. Semantic Notes (Non-Binding)

  • Preserves strict logical reasoning
  • Prevents implicit truthiness bugs
  • Serves as a base for logical variables