Unique Name Assumption¶
A semantic assumption that distinct individual names denote distinct entities, making the interpretation of names injective within the formal reasoning system.
Core Idea¶
The unique name assumption turns a syntactic distinction into a semantic one. If two individual constants have different names, their denotations must be different domain elements. This simplifies many database and logic inferences by eliminating possible coreference among unequal constants.
Not all knowledge-representation languages adopt it. In OWL, distinct identifiers can denote the same individual unless sameness or difference is asserted or derived. Moving data between reasoning regimes therefore requires stating the naming policy rather than inferring it from identifier appearance.
Scope of Application¶
- Description logics. Controls whether different individual constants may share a denotation.
- Ontology integration. Determines whether identifiers from multiple sources can represent one entity.
- Database semantics. Explains a common identity simplification in relational reasoning.
- Semantic-web interoperability. Prevents accidental import of inequality into a language that permits coreference.
Clarity¶
State the formal language, kind of names covered, interpretation semantics, and whether inequality is global, local, explicit, or absent. Test entailment in the actual logic; different character sequences are evidence of syntax, not automatically of distinct referents. Inclusion test: Require a formal vocabulary of individual names and a semantic rule making the denotation map injective across distinct names. Exclusion test: Exclude database keys, ordinary naming conventions, lexical uniqueness, and explicit inequality assertions limited to selected pairs. Nearest boundary: The closed-world assumption treats absent facts as false under a reasoning regime; the unique name assumption treats distinct individual constants as denoting distinct entities. Exit condition: The identity disappears when distinct names may corefer unless explicitly separated, or when uniqueness concerns records or strings rather than semantic denotation. Common misclassifications: It is not a requirement that human-readable names be globally unique. It is not a database primary-key constraint, though database practice often approximates its effect. It is not the closed-world assumption. It is not equivalent to asserting differentFrom for one selected pair of individuals. Nearest named distinctions: Closed-world assumption: Closed-world reasoning concerns unasserted facts, not denotational identity of different names. Database key: A key distinguishes records under a schema; UNA constrains semantic models of individual constants. owl:sameAs: sameAs explicitly identifies two names, which is meaningful precisely because OWL lacks global UNA. Unique identifier: Operational uniqueness of an identifier does not alone specify whether other identifiers may co-refer.
Manages Complexity¶
The assumption removes an entire family of possible models in which names co-refer. That compression makes equality reasoning cheaper and query results sharper, while also revealing the cost: aliases and cross-source identity must be represented through exceptions or cannot be represented faithfully.
Abstract Reasoning¶
- Identify the individual constants and the interpretation in which they receive denotations.
- Check the language specification for a global injectivity rule on names.
- Separate that rule from explicit same-entity or different-entity assertions.
- Trace how the policy changes satisfiability, equality entailments, and query answers.
- When integrating systems, reconcile their naming assumptions before merging identifiers.
Knowledge Transfer¶
The transferable cargo is an injectivity constraint on the mapping from formal names to individuals and its consequences for equality reasoning. It transfers between logic systems only when the same class of constants and semantic rule are preserved; it stops at informal labels, record keys, or conventions lacking model-theoretic denotation.
Relationships to Other Abstractions¶
Current abstraction Unique Name Assumption Domain-specific
Parents (1) — more general patterns this builds on
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Unique Name Assumption presupposes Identity Test Prime
Unique Name Assumption presupposes Identity Test because distinct names are stipulated to pass a distinct-referent identity test.
Hierarchy path (1) — routes to 1 parentless root
- Unique Name Assumption → Identity Test → Criteria of Individuation
Neighborhood in Abstraction Space¶
Unique Name Assumption sits in a moderately populated region (57th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Logical Connectives & Formal Systems (13 abstractions)
Nearest neighbors
- Bijective proof — 0.86
- Naming System — 0.85
- String kernel — 0.85
- Elementary substructure — 0.85
- U-Form — 0.85
Computed from structural-signature embeddings · 2026-10-08