Is this a rule of all first-order logic?

No. Ordinary semantics allow different constants to denote the same individual unless constrained otherwise.

Does a globally unique identifier guarantee a unique real-world referent?

It can identify a record reliably, but multiple records may still refer to one thing.

Can distinctness be local?

Yes. A model can explicitly distinguish selected individuals without imposing a global convention on every name.

AI Glossary / Graphs and symbolic AI / Advanced

Unique-names assumption

Definition

The unique-names assumption is the convention that different names denote different individuals. For distinct constant symbols a and b, it permits the conclusion a≠b without a separate statement about that pair. Some logical frameworks extend the convention to distinct ground terms, including compound terms with no variables.

What it means

A name is a symbol used to refer to something; the thing it denotes is its referent. Different symbols do not inherently guarantee different referents. Two systems may assign different identifiers to the same supplier, or one person may be known by two names.
Adopting the unique-names assumption rules out such shared reference within its stated scope. This can simplify reasoning when identifiers are deliberately assigned to distinct modeled entities. It can also produce incorrect conclusions when aliases or duplicate records are possible. The assumption is a modeling choice, not evidence obtained merely by comparing spelling.

How it works

For a finite collection of distinct constants, the assumption can be represented by pairwise inequalities. With n names there are n(n−1)/2 unordered pairs. A system may enforce the convention semantically rather than storing every inequality explicitly.
Equality reasoning must remain consistent with it. If a theory both requires a≠b and asserts a=b, it has no model under ordinary classical semantics. When applying the convention to compound ground terms, the framework must also specify how function symbols and their arguments determine identity; a blanket assumption is inappropriate for interpreted arithmetic expressions.
OWL does not generally infer distinct individuals from different individual names. Its SameIndividual and DifferentIndividuals constructs can state equality and inequality. Other axioms can also imply identity relationships or distinctions. Failing to assume inequality does not mean assuming equality: either possibility may remain open until the ontology provides enough information.

Three practical examples

A warehouse planning model uses box1, box2, and box3 for three verified physical boxes. Treating those names as distinct supports counting and rules that require different objects.
Two procurement systems use separate vendor identifiers for one supplier. Applying a blanket unique-names assumption to their merged data would mistakenly force the supplier to be represented as two different entities.
A fictional puzzle explicitly names four different participants. Encoding their names as distinct prevents a logical solution from satisfying several participant roles using a single individual.

Think of it this way

Picture three labels on a desk. The labels could identify three separate folders, or two labels might belong to the same folder. The unique-names assumption says that each different label identifies a different folder. It does not inspect the folders to establish that this is actually true.

Worked example

Suppose a small knowledge base contains three names, a, b, and c, each asserted to be a supplier. No other facts distinguish or equate them. Consider only the identity relationships among the three named referents, not the total size of the world.
Without the unique-names assumption, five patterns are possible: all three names refer to one supplier; only a and b share a supplier; only a and c share one; only b and c share one; or all three refer to different suppliers. Thus the names can identify one, two, or three distinct suppliers.
With the assumption, only the fifth pattern remains. The required inequalities are a≠b, a≠c, and b≠c: 3×2/2=3 unordered pairs.
Instead, suppose the theory has no blanket assumption and explicitly states a=b. Two patterns remain: all three names share a referent, or a and b share one while c denotes another. Adding a≠c leaves exactly two distinct named suppliers.
Now combine a=b with the original unique-names assumption. The result is inconsistent because that assumption also requires a≠b. It does not silently merge the records while preserving the assumption.
Finally, three distinct named suppliers do not establish that only three suppliers exist. An unnamed fourth supplier remains possible unless another statement closes the relevant domain or supplier class.

Illustrative case study

A fictional service company combines maintenance records from two acquired businesses. One system identifies a machine as asset_A17, while another identifies it as unit_B42. Staff suspect that the records describe the same physical machine, but matching locations alone is not conclusive.
The integration team separates record identity from machine identity. The two source records are distinct records even if their subject is one machine. After checking serial numbers and provenance, the team can state an appropriate relationship between their machine identifiers rather than assuming identity from a partial match.
For verified inventory items, a local distinctness convention may still be useful. The team documents that scope and tests merges for contradictory equality and inequality assertions. This fictional example illustrates an identity-modeling decision; it does not claim an automated matching system has established the facts.

Common misconceptions and mistakes

The assumption does not say every object has a name. Nor does it say that all objects have already been listed. Those are separate completeness or domain-closure questions.
It is not the closed-world assumption, which concerns what to conclude from absent information. Name distinctness and missing facts address different issues.
Different records can describe the same entity. Conversely, matching display names can belong to different entities. Database keys, human-readable labels, and real-world identity should not be treated as interchangeable.
Without the assumption, a=b is not automatically true. The equality may simply be undecided.

Business use

Clarify identity assumptions when connecting knowledge graphs, planning systems, product catalogs, or operational databases. They affect counts, duplicate detection, resource allocation, and rules requiring distinct participants. Record where distinctness is guaranteed and where aliases are allowed. For external data, preserve provenance and distinguish a claim about an entity from the identity of the record containing that claim.

Check your understanding

How many identity patterns exist for the three unconstrained names in the example?

Answer: Five.

What remains after a=b and a≠c?

Answer: Two distinct named referents: the shared a/b supplier and the c supplier.

Does three distinct names exclude unnamed objects?

Answer: No. Distinctness does not establish domain closure.

Related terms

Unique action axioms
Domain closure
Closed-world assumption
Ontology
Equality
entity resolution
OWL
identifier
knowledge graph

Learn next

Compare equality, explicit inequality, and an unresolved identity relationship. Then study how domain closure and open-world reasoning affect counts and consistency in a small ontology.

Sources

Poole and Mackworth, Unique Names Assumption, formal convention and ground-term scope: https://artint.info/2e/html2e/ArtInt2e.Ch13.S7.SS2.html W3C, OWL 2 Primer, Section 4.7 on equality and inequality of individuals: https://www.w3.org/TR/owl2-primer/#Equality_and_Inequality_of_Individuals AIMA glossary, unique-names assumption: https://github.com/aimacode/aima-glossary

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