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.
Structural Signature¶
Sig role-phrases:
- Individual names — Provide the syntactically distinct constants whose denotations are compared. It is carrier. Counterfactual: Different spellings outside a formal language do not automatically count as constants.
- Interpretation domain — Contains entities to which names are mapped. It is semantics. Counterfactual: Without an interpretation, name difference remains purely syntactic.
- Denotation function — Maps every individual name to a domain element. It is relation. Counterfactual: The assumption constrains this map rather than string equality itself.
- Injectivity condition — Requires unequal names to have unequal denotations. It is invariant. Counterfactual: If two names can corefer, the global assumption is absent.
- Equality assertions — Permit a logic without UNA to state sameness or difference case by case. It is contrast. Counterfactual: Explicit inequality is not equivalent to adopting UNA for every pair.
- Reasoning regime — Determines entailments and consistency consequences of the naming policy. It is validity. Counterfactual: Importing UNA silently can change query answers or make identity data inconsistent.
What It Is Not¶
- 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.
- Closest near-miss. 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.
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.
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.
Examples¶
Canonical¶
In a knowledge language with UNA, constants alice and a_smith are interpreted as different individuals solely because the names differ, unless the formalism provides and applies an exception mechanism.
Mapped back: names → distinct; denotation map → injective; entailed relation → different individuals.
Applied / In Practice¶
An OWL ontology contains two IRIs with no sameAs or differentFrom assertion; their distinct spelling alone does not entail that they denote different individuals.
Mapped back: language → OWL; names → distinct; difference entailment → absent.
Structural Tensions¶
T1 — Simpler Identity Reasoning versus Coreference Expressiveness. UNA removes possible name merges but can misrepresent integrated data containing aliases.
Diagnostic: Can two sources legitimately use different identifiers for one entity?
T2 — Implicit Inequality versus Explicit Provenance. Global difference is convenient, whereas explicit identity assertions expose which distinctions are actually supported.
Diagnostic: Is inequality a semantic default or an asserted fact for this pair?
Structural–Framed Character¶
Unique Name Assumption is hybrid: structurally an injective naming constraint and framed by formal knowledge-representation semantics.
Structural Core vs. Domain Accent¶
The skeleton is a map from symbols to referents constrained to be one-to-one. Logic supplies interpretations, individual constants, equality, satisfiability, entailment, open-world behavior, and the system-specific treatment of explicit identity statements.
Instantiates / Related Primes¶
This entry presupposes Identity Test.
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Approved root. No reviewed parent entails this exact semantic injectivity policy.
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Related — identity test, naming convention, closed-world assumption, open-world assumption, owl:sameAs, and database key. These address nearby questions without equating distinct syntax with distinct denotation globally.
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.Every reviewed Unique Name Assumption instance depends on the parent role: distinct names are stipulated to pass a distinct-referent identity test. Removing that role makes the frozen child identity undefined or changes it into a different abstraction. Identity Test can occur without Unique Name Assumption, so the relation is dependency rather than subsumption.
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
Not to Be Confused With¶
- Closed-world assumption. Tell: Closed-world reasoning concerns unasserted facts, not denotational identity of different names.
- Database key. Tell: A key distinguishes records under a schema; UNA constrains semantic models of individual constants.
- owl:sameAs. Tell: sameAs explicitly identifies two names, which is meaningful precisely because OWL lacks global UNA.
- Unique identifier. Tell: Operational uniqueness of an identifier does not alone specify whether other identifiers may co-refer.
References¶
- Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Unique_name_assumption (revision 1298445220).
- Preserved source candidate: http://www.aaai.org/ocs/index.php/AAAI/AAAI10/paper/view/1931
- Preserved source candidate: http://www.w3.org/TR/owl-ref/
The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.