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CompositeDomain — Semantic Specification

1. Definition

A CompositeDomain is a ValueDomain that defines admissibility by combining multiple ValueDomains using explicit logical composition.

It enables multidimensional or constrained value spaces without redefining primitive domains.

2. Declaration

A CompositeDomain exists as a specialization that:

  • Contains two or more ValueDomains
  • Declares a composition operator
  • Applies deterministic evaluation

Minimal declaration requirements:

  • A finite set of component domains
  • A declared composition rule

No implicit precedence or coercion is allowed.

3. Semantic Invariants

D1: Domain Closure

All components MUST be valid ValueDomains.

D2: Deterministic Composition

Given the same input, composition MUST yield the same admissibility result.

D3: No Value Transformation

CompositeDomain MUST NOT alter values.

D4: Explicit Semantics

Composition logic MUST be explicit and fixed.

4. Composition Operators

Allowed operators:

  • AND — value must satisfy all domains
  • OR — value must satisfy at least one domain
  • XOR — value must satisfy exactly one domain
  • NOT — negation of a single domain

5. Negative Definition

What CompositeDomain is NOT.

  • Not a new primitive domain
  • Not probabilistic
  • Not fuzzy
  • Not hierarchical
  • Not order-dependent unless explicitly stated

6. Impossibilities

  • Empty component sets are invalid
  • Circular domain definitions are invalid
  • Implicit coercion between domains is invalid
  • Conflicting composition rules are invalid

7. Boundary Conditions

  • Single-domain composite: Valid but redundant.

  • Contradictory domains: CompositeDomain may admit no values.

  • Evaluation order: Undefined unless explicitly stated.

8. Example (Non-Normative)

Composite = NumericDomain(0 ≤ x ≤ 1) AND Not(IntegerDomain)

validate(0.5) → admissible
validate(1)   → inadmissible

9. Validation Rules

  • Static: All component domains must be valid.

  • Runtime: Value admissibility follows declared composition logic.

10. Semantic Notes (Non-Binding)

  • Enables expressive constraint modeling
  • Preserves domain orthogonality
  • Avoids explosion of specialized domain types
  • Supports future extensions (e.g., temporal domains)