Equivalence relationships like identical are reflexive, symmetric, and transitive. Set theory constructs sets without duplicates, limiting each set to a single cardinality. The identical predicate determines if two references (Ref1 and Ref2) refer to the same thing by checking if Ref1=Ref2. Global Unique Singular Identifiers (GUSIs) are computational representations that can be placed in one-to-one correspondence with things, allowing determination of identity through matching GUSIs. However, managing identity on a global scale poses challenges around the practical implementation of a system with GUSIs.

1. Equivalence: Identical is an equivalence
relationship: reflexive, symmetric, transitive.
Cardinality: Set theory constructor (no Identical Predicate: When is it true that
duplicates) constrains set to cardinality of one. Identical(Ref1, Ref2); i.e., Ref1=Ref2?
Behavior (Subsitutability):
f(Ref1) = f(Ref2) for any function f.
Point-to-point path finding (using transitivity
property & chain of intermediate references) The problem: Do two references
Identification refer to one and the same thing? Historical: no longer true
strategies
Hub and spoke method
The solution: involves (i) references, Speculative or predictive: not yet true
Global: recognized using global identifiers. "Real world"
(ii) an identical predicate, (iii) Global
throughout the Universe Unique Singular Identifiers (GUSI) information types Opinionated or subjective:
Global Unique Singular Identifiers true to some people & not others
Unique: different things (GUSI): a class of computational surrogates
cannot have the same GUSI than can be placed in a one-to-one Fictional or false: not true at all
correspondence with things they denote.
Singular: a thing cannot be
E.g., one unsolvable
denoted by more than one
GUSI identity problem. Enterprise | organization unit
Core identity proposition: If the GUSIs exist,
references are identical if the GUSIs match, and the Business sector
GUSIs must match if the references are identical.
Subject matter
Computational surrogates (future) might include Application
Domains: many ways
pictures, fingerprints, voice prints, retinal scans. of grouping information.
Identical predicate implementation more complex. Document (What is a document?)
Geographic units
Theoretical: more things than numbers that
can be represented in computer systems (?). Culture
(However, for any specific case the set of
things of interest is likely to be finite.) Combinations of domains, etc.
GUSI management: (i) Maintaining global recognition, Contains information
uniqueness, & singularity requires a global, omniscient about itself.
naming authority (impractical); (ii) domain differences on Why the proposed idealized
GUSI implementations and identical definitions. Some information is not
solution doesn't work on computer media
Identical predicate: (i) managing transitivity in a vast universe is Cyberspace: information
hard; (ii) identification heuristics and uncertainty resolution; (iii) a management in computer systems. Support local syntax: ensure mechanical
hidden step in a larger process and hard to verify correctness.
William Kent: distinguishability among local markups.
Absence of GUSIs and other suitable identifiers: Practical The unsolvable identity problem* A mess of mappings, constraints,
(i) many databases have their own IDs; (ii) documents inheritance rules, and exceptions.
(and things?) may not have unique IDs at all.
Evolution of identity: GSUIs may need to merge; one
may need to replaced by several -- hard to manage. What is this? (primary, but not useful question)
Relationships:
Semantic headaches: the semantics of (i) situational or connections among things
What do I want? (looking for; too vague)
relative identity, (ii) identity evolution, (iii) what can be identified,
and (iv) versions and copies, do not admit of general solutions. Attributes: connections
between things and data values How to tell if two things are the same?
(same? or identical?)
Do data values represent things,
or ideas of things (concepts)? How to specify "One and the same thing"?
Graph theory (ambiguities: arc, node, graph, Same to you? (might depend on the situation)
simple graph, complex graph, tree, etc.) Data values
Is Identity dependent on time?
Use of controlled vocabularies The identity problem: the first problem Other properties? ("inherent qualities"?)
(inter-indexer consistency in of identity is the identity of the problem
application unlikely to be 100%) What does it mean to refer to something?
(What is a reference? Do two references refer
XML the Data Format (and data models) to one and the same thing?)
XML the Data Vocabulary ("languages") Individuals (people, places, things, organizations, etc.)
Examples
XML the Application (use of tags, vocals, XML examples Computer stuff (hardware, software, events and logs,
tools to make SOMETHING happen) etc.)
XML the All-encompassing Technology (plethora Data values?
of standards: W3C XML, XDR, XPath, XQuery, XSLT,
XML RPC, formal data models, APIs, etc.) What is identifiable? Aggregates? (Set theory: set is defined by its members)
Identity & differences; Unreals? (inhabitants of fiction, dreams, imagination)
versions & copies Identity problem or the
Indistinguishables? (somewhere
generalized dictionary problem?
Names & references someone cares about the distinction)
Any specific word?
* Kent, W., The unsolvable identity problem, Proceedings Extreme Markup Languages 2003, Retrieved
W.L. Anderson, 2013, CC-BY
2013-02-10 from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.95.6902&rep=rep1&type=pdf