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Copyright © 1998, American Medical Informatics Association Representing Thoughts, Words, and Things in the UMLS Affiliations of the authors: Stanford University, Stanford, California (KEC, DEO, EHS); Oregon Health Sciences University, Portland, Oregon and College of American Pathologists, Northfield, Illinois (KAS); Veterans Administration Health Care System, Palo Alto, California (DEO). Correspondence and reprints: Keith E. Campbell, MD, PhD, Section on Medical
Informatics, Stanford University School of Medicine, Stanford, CA
94305-5479. Received February 3, 1998; Accepted April 17, 1998. This article has been cited by other articles in PMC.Abstract The authors describe a framework, based on the
Ogden-Richards semiotic triangle, for understanding the relationship between
the Unified Medical Language System (UMLS) and the source terminologies from
which the UMLS derives its content. They pay particular attention to UMLS's
Concept Unique Identifier (CUI) and the sense of “meaning” it
represents as contrasted with the sense of “meaning” represented
by the source terminologies. The CUI takes on emergent meaning through linkage
to terms in different terminology systems. In some cases, a CUI's emergent
meaning can differ significantly from the original sources' intended meanings
of terms linked by that CUI. Identification of these different senses of
meaning within the UMLS is consistent with historical themes of semantic
interpretation of language. Examination of the UMLS within such a historical
framework makes it possible to better understand the strengths and limitations
of the UMLS approach for integrating disparate terminologic systems and to
provide a model, or theoretic foundation, for evaluating the UMLS as a
Possible World—that is, as a mathematical formalism that represents
propositions about some perspective or interpretation of the physical
world.
Many informatics developers have struggled to understand how best to
leverage the Unified Medical Language System (UMLS) in their applications. One
fundamental decision faced by these developers is whether to treat the UMLS as
if it were a coding system unto itself—by using the UMLS Concept Unique
Identifier (CUI) to represent concepts communicated in coded form and archived
in data repositories—or whether to rely directly on one or more of the
UMLS source terminologies for concept representation and use the UMLS as a
system for providing appropriate interoperability between terminologies, as
when trying to “facilitate the development of conceptual connections
between users and relevant machine-readable
information.”1 We previously argued that evaluating the UMLS as if it were itself a coding
system places it in a competitive position with the very sources from which it
is derived and does not help us understand the unique value that the UMLS
intends to provide.2
Here we seek to characterize other consequences of treating the UMLS as if it
were a coding system, by describing the limitations of communication inherent
in our language and the implications that those limitations have on
understanding the “meaning” of terms represented by a CUI. Because the UMLS is founded on language, we present first a historical
framework for understanding the relationships among the words we speak and
write, the thoughts we are trying to express with our language, and the things
to which our words and our thoughts refer. Next, we focus on the UMLS approach
to concept representation and terminology specification, considering the UMLS
in the context of this framework for thoughts, words, and meaning. By seeking
a historical perspective, we intend to demonstrate the timeless nature of
several principles of semantic interpretation and their applicability to the
UMLS. Thoughts, Words, and Things How thoughts, words, and
things* relate to one
another has been a recurrent theme in scholarly works of philosophy and
language from as early as Plato to the modern era. Plato dealt with the
question of the proper naming of things in Cratylus, a dialog in
which the participants argue over whether names are correct simply because
they are used by convention (conventionalist view) or whether, in an ideal
language, names would be most correct if they resemble or naturally describe
the entities they name (naturalist
view).4 Plato
himself seems to propose that neither of these views is completely accurate.
In an optimal world, the purpose of names would be to ensure that a particular
expression will make everybody think of one and only one thing. Plato,
however, was doubtful that perfect names, which would reflect the character of
the things they represent could ever be given, because things are continually
changing. If things are continually changing, then there is no way to know
what a thing is or what it is really like. Aristotle went beyond the question of names and was interested in
definitions. His notion of definition was not, as we usually think of it,
simply the linguistic meaning of a word but was meant to explain clearly what
a thing is by being a statement of the “essence” of the
entity.5 Aristotle
believed that to say what something is, one must say why
something is; therefore, his definitions were causal. An Aristotelian
definition is given by specifying the genus and differentia of individuals and
then using logical arguments to categorize those individuals on the basis of
their definitions. By identifying the common definitional properties of
similar individuals, the definition explains why they are members of the same
kind. Representing terms relevant to health care data using an Aristotelian
approach can provide a logical foundation for representing clinical
data6; however, such
an Aristotelian foundation is not sufficient. The language used to represent
the terms of an Aristotelian system must be sufficiently precise to allow the
terms to be reproducibly understood and applied. We cannot ignore, however,
the unavoidable limitations of communicating meaning via language and the
inherit ambiguities created by implicit exchange of different
“senses” of meaning. Understanding such ambiguities was a topic that concerned Gottlob Frege
(1848-1925), a German philosopher and logician. Frege was not only one of the
founders of mathematical logic and set theory but also a significant
contributor to the philosophy of
language.7,8
Frege studied the meaning of proper names and concept words in his essay
“On Sinn and Bedeutung,” in which he distinguished between two
types of meaning: thought content and referent. We look at Frege's ideas,
particularly the two types of meaning he articulated, as a basis for
understanding the semantic framework of the UMLS. Ogden and Richards
popularized the importance of understanding the difficulties posed by these
different senses of meaning and graphically illustrated the relationship
between language, thought content, and referent in a diagram commonly referred
to as either the semiotic triangle or the meaning triangle
(Figure 1 The diagram shows that, although written or spoken symbols (words) cannot
completely capture the essence of a reference (thought) or of a referent
(thing), there is a correspondence among them. Either a word or an object can
inspire a thought, and people may endeavor to express their thoughts with
words or by identifying objects in the world. The relationship between a word
and a thing is indirect, however. The link can be completed only when an
interpreter (usually a person) processes the word, which invokes a
corresponding thought, and then links that thought to a thing in the world
(the “referent”). This diagram is seductive in its simplicity. By implying a one-to-one relationship between each pair of members in the
triangle, this simple diagram masks hidden complexity. Ogden and Richards
alluded to this complexity by the dotted line between a symbol and a referent,
indicating that the link between a symbol and a referent can only be made
indirectly through an interpreter, but the notion that a symbol does—or
could—refer to a single thought and that a thought does—or
could—refer to a single referent is a fallacy. Many recognize that we
live in a world where referential complexities lead to difficulties in
communication. In Lewis Carroll's Alice Through the Looking Glass
Humpty Dumpty insists that he can make words mean whatever he wants them to
mean. In Plato's Cratylus, Socrates argues that it is not enough to
try to understand what a thing is, based on its name, because the name-givers
may have been living in ancient times, and the name reflects only what the
name-givers thought was the nature of reality then; however, they may have
been wrong. Thus, it has been historically recognized that multiple terms may
refer to the same object or idea, a single term may refer ambiguously to more
than one object or idea, and terms may be confusing because they are out of
date. It is within this context that we seek solutions to improve our ability
to communicate about biomedical concepts. In professions where ambiguous communication can have deadly consequences,
as in medicine, there is a strong desire to have one-to-one relationships
between thoughts, words, and things among all the participants (interpreters)
in the process. In a supplement to The Meaning of Meaning by Ogden
and Richards, a physician named Crookshank recognized the clarity of
communication that would result if medicine could develop an unambiguous
relationship between thoughts, words, and things. He accordingly chastised the
medical profession:
Crookshank's goal of improving communication is laudable and has proved
effective in the “exact sciences” and in the legal world (for
example, in the preparation of formal contracts as discussed by
Eco10). Such
precision is an unobtainable goal for medicine, however, if for no other
reason than the imperfectability of human beings and the huge regional
variations in disease and its manifestations. Even more pertinent, of course,
is the magnitude of medical knowledge that must be mastered to approach the
understanding necessary to delineate completely all the words used in the
profession, all the possible thoughts that might be invoked by those words,
and all the possible things to which those thoughts might refer. Another factor that complicates our efforts to improve communication is the
vertical nature of medicine, as described by
Blois.11 He points
out that medical knowledge (and hence communication regarding medicine) is
vertically organized, in that mastery of the discipline requires a corpus of
knowledge that ranges from the foundational and relatively exact sciences of
physics and chemistry (which have precise symbolic mechanisms of communication
such as the periodic table of the elements) to psychology and sociology (where
the elements of discourse are often intangible and difficult to communicate).
Hence, our ability to be precise in medical communication is challenged as one
goes “up” this vertical scale from basic sciences to the social
and psychological milieu in which a patient functions and is assessed. Although we argue that the complete delineation of the thoughts, words, and
things relevant to medicine, and their subsequent encoding, are laudable but
elusive goals, we readily concede that the pursuit of such a codification,
such as the UMLS is undertaking, will improve the clarity with which we
communicate. To optimize the utility of such a codification, however, it is
critical that we understand its limitations. Unrecognized ambiguity created by
interchanging different “senses” of meaning is one such limitation
that we discuss in the following sections. Extensional and Intensional Meaning In a classic example by Frege, the names “morning star” and
“evening star” are expressions that refer indirectly to the same
physical object, the planet Venus. Although today we know this is the case,
there was a time when people were not aware of the correspondence between the
“physical objects” implied by the two terms. Our interpretation of
the world is shaped by our experiences, and they in turn determine how we
communicate with one another. Our ability to understand one another depends on
having sufficient shared experiences that we can invoke common thoughts when
other people confront us with appropriate words and things. Although in one
sense we can say that “morning star,” “evening star,”
and “Venus” are equivalent (that is, they have the same meaning in
the sense that they all refer to the same planet), one can also say that
“morning star,” “evening star,” and
“Venus” are not equivalent (in the sense that more information is
connoted by these names than simply the physical objects to which they refer,
such as when the entity can be observed and, perhaps, the experiences of the
observer). In such statements, Frege recognized a puzzle: How can we say the
same thing about the same objects but mean different things? Consider the
following two expressions:
These expressions refer to the same object (Venus), yet the sense of
meaning conveyed by the two expressions is very different (consider the
implicit time of day conveyed by the expressions). Frege explained this puzzle
by recognizing that the “meaning” of expressions can be divided
into two components: On the one hand there are the physical objects to which
the expression refers (the expression's extensional component) and on
the other there are the characteristic features of the physical object used to
identify it (the expression's intensional
component).† Understanding
the interrelationship between intensional and extensional meaning is essential
to understanding the “senses” of meaning represented within the
UMLS. Only with this understanding can we know when symbols (such as morning
star and evening star) can be substituted for one another without loss of
truth. Figure 2
The UMLS as a Possible World The Ogden-Richards triangle has elucidated the relationship between
thoughts, words, and things in the corporeal world by providing a conceptual
frame-work that we can use to better understand our use of the language. The
UMLS is an example of an artifact that embodies these same relationships in
what has been called a Possible World, an artificial system in which
relationships can be formally codified and the truth values of these
relationships can be
evaluated.‡ The notion of
Possible Worlds originated with the 17th-century German philosopher Gottfried
Leibniz (1646-1716), who used the notion for theologic purposes. Leibniz said
that God could create only logically possible worlds, but that being
omniscient and beneficent, he would actualize the best of all possible
worlds.14 Modern
logicians have abandoned the theologic implications in employing the idea of
Possible Worlds. One approach taken by formal semanticists, dating back at
least to the work of the logician Jørgen Jørgensen in the
1930s,15 is to say
that a Possible World is simply a set of propositions. This approach has
subsequently been much discussed in the philosophy and artificial intelligence
literatures (see, for example, Herbert Simon's classic book The Sciences
of the
Artificial16).
In describing the UMLS as a Possible World, we state that it is possible that
there exists a perspective on the world where the correspondence among words,
thoughts, and things are exactly as represented by propositions within the
UMLS.§ We also claim that the UMLS contains all the characteristics of the
Ogden-Richards triangle. This should not be surprising, since the approach
taken in developing the UMLS was founded on the belief that the essential
properties of biomedicine necessary to construct the UMLS would reveal
themselves via the properties of language used to describe the
discipline,17 and
the Ogden-Richards triangle was developed to explain the relationship of
language to thoughts and to the world. Thus, the development of the UMLS was
empirically driven. Rather than attempting the creation of a system de novo,
the developers collected the language that others had codified into
terminologic systems, provided a framework where the intension (connotation)
of terms of those systems could be preserved, and unified those systems by
providing a representation of extensional
meaning by collecting
abstract concepts into sets that can be interpreted to represent their
extension.¶These extensional sets are codified by the Concept Unique
Identifier (CUI) in the UMLS. We argue that the “meaning” of
this identifier is only understandable extensionally, by examining the
characteristics shared by all abstract concepts linked by a CUI. We will
illustrate the correspondence of the UMLS and the Ogden-Richards triangle by
using the notion of “aspirin” as a prototypical example in the
following sections. Words Words represent written and spoken communication by which we convey meaning
to one another. In an “artificial” world, such as the UMLS, words
provide a link between the realm in which we live and the symbolic world in
which computer programs operate. As such, the notion of words that are part of
our language expands to include the notion of symbols that represent a source
terminology's “representation,” such as a Systematized
Nomenclature of Medicine (SNOMED) term
code.18 Table 1 presents phrases in
the UMLS that correspond to the concept C0004057 named Aspirin. Note that the
entries include terms in several languages, since the UMLS contains entries in
English, French, German, Spanish, and Portuguese. Although the initial set of
phrases came from the source terminologies, UMLS provides added value by
cataloging preferred forms and categorizing lexical variants by word order and
by case case differences.
Thoughts When developers of source terminologies developed their systems, they had
very specific thoughts about what the individual terms “meant” (in
the intensional sense) with respect to the terminology they were developing
and the human beings who would interact with those systems. Although we cannot
directly know what was in the minds of the developers of the source
terminologies, the UMLS developers have used clues embodied within the sources
to try to infer what those thoughts were and to try to codify those thoughts
within the UMLS. These clues take several forms: the term used by a source to
describe the thought; the synonyms used by a source to describe other
statements that its developers considered equivalent to the thought; and any
formal or informal relationships used by the developers to relate terms within
the terminologic system to one another. Some of the informal relationships had
to be inferred from processing the typesetting tapes for a particular source,
using constructs such as how many tabs appeared before the word, whether the
word was in bold or italics, and what page of the printed book the word
occurred on. Figures Figures33
It is obvious that the intension associated with a term in a source
terminology is represented at least in part by its location in a hierarchy and
by decisions made regarding synonyms and nonsynonyms. Aspirin in the CRISP
Thesaurus is a chemical; it is also a centrally acting drug that has
antirheumatic, anti-inflammatory, analgesic, and antipyretic properties.
Similarly, the UMLS equivalent of aspirin in SNOMED, acetylsalicylic acid, is
a chemical. It is also a drug with several of the same properties that it has
in the CRISP Thesaurus: It is a centrally acting agent, an analgesic, and an
antipyretic. On the other hand, in SNOMED, acetylsalicylic acid is not
synonymous with two other UMLS equivalents of aspirin, Easprin and Zorprin,
because the first is a generic drug and the other two are proprietary drugs.
Thus, in SNOMED, the intension of aspirin is clearly not the same as the
intension of Easprin, yet aspirin and Easprin are linked to the same CUI. It
may even be argued that there are subtle differences in the intension of
aspirin in CRISP and SNOMED, yet these differences are obscured or lost when
one moves from the source terminology to the CUI. It is clear that the intensional meanings, or connotations, of terms in the
different sources are distinct. Some source terminologies, such as SNOMED, can
have very precise semantics, differentiating between the observation of a
particular pathologic change (such as a fracture) and the diagnostic statement
that a fracture may exist in a particular patient affecting a particular bone.
SNOMED maintains these distinctions by maintaining independent hierarchies
(such as topography, morphology, procedures, and diagnoses) that embody
different intensions. Other terminologies, such as the National Library of
Medicine's Medical Subject Headings
(MeSH),20 have no
need for such detailed specificity, and thus the intensional meanings of
similar phrases in MeSH cannot be interpreted in the same way that they might
be in SNOMED. For example, “gastrointestinal transit” in MeSH is
used to denote both the physiologic function and the diagnostic
measure.21 SNOMED
would use separate codes to differentiate these two notions, by putting a
“gastrointestinal transit” term that represented physiologic
function into the function axis and putting a “gastrointestinal
transit” term into the procedure axis that represented the act of
performing the diagnostic measure. The point here is not that the intensional meanings of phrases in SNOMED
are somehow more correct or desirable than the intensional meanings of phrases
in MeSH. MeSH and SNOMED are different because they were intended for
different purposes. Thus, for the UMLS to meet its goal of integrating sources
such as SNOMED and MeSH into a useful framework, it must represent the
different intensions of the sources while also providing appropriate
integration. Developers of the UMLS recognized this requirement to represent the notion
of meaning relative to the scope, granularity, context (hierarchy), synonyms,
and annotations of the source
terminologies,21
and we believe that this aspect of their design has been successful. For each
source, the UMLS explicitly represents the hierarchic context in which the
terms are encountered and links those terms to other “extensionally
equivalent” terms (in this case, all terms linked to the referent
“Aspirin”) from all the UMLS sources. We discuss these extensional
representations in the next section. Things To complete the Ogden-Richards triangle, the UMLS must have a
representation of “things.” A museum may represent things by
collecting example “prototypical” artifacts from around the world
and making them available for inspection and experimentation. For the UMLS,
the task is somewhat more complicated, since many of the “things”
it must represent have no physical manifestation and are comprehensible only
in the abstract. Thus, the UMLS uses an abstract notion of
“concepts” to represent classes of “things” that can
in some sense be considered equivalent, and it provides a CUI as a means of
codifying the extension of these classes. It can be argued that the complete
notion of what these CUIs represent is understandable only extensionally, as
the characteristics shared by all the intensional representations linked
together via a common CUI, including both relationships or annotations derived
directly from UMLS sources themselves as well as other relationships or
annotations that are provided during UMLS construction. Figure 5
In Figure 5 This observation does not mean that we believe that the focus of
representation in the UMLS is incorrect, nor do we mean that this focus is
incapable of evolving to meet the needs of the consumers of the
UMLS—quite the contrary. Because the representational framework of the
UMLS is consistent with the historical themes of interpretation and meaning,
and because it provides a framework for linking thoughts, words, and things
relevant to the medical domain into a codified system that represents a
Possible World, we can begin to have a dialogue about our intensional and
extensional representational needs. We can thereby determine whether the
current Possible World is an appropriate embodiment of our needs or whether
the content of the UMLS needs to evolve in a particular way to better meet our
needs. By providing a formal framework where we can begin to ask these
questions of specific concepts, the UMLS enables a dialogue about the meaning
of “aspirin” that we could not have had without the creation of a
Possible World as a starting point. Winograd refers to such formal frameworks
as systematic
domains,22 a
structured formal representation that provides precise and unambiguous
description of the tasks (the process of assigning “meaning” in
the case of the UMLS) and forms the basis for tools that aid in communication
and the cooperative accumulation of knowledge. We can begin cooperative accumulation of knowledge through meaningful
evaluation of the UMLS, but the evaluation must be appropriate for its
framework, content, and purpose. Through such an evaluate-and-revise cycle, we
can approach a codification of medical language that will improve the clarity
with which we communicate, even if it is impossible to achieve a codification
that is entirely unambiguous. Appropriateness of a Possible World Terms that share the same CUI are equivalent in a particular Possible
World—that is, in the Possible World represented by the UMLS. Any
evaluation of the UMLS should include an evaluation of the appropriateness of
this Possible World. However, evaluators can perform such a study well only if
they have an understanding of the Possible World the UMLS intends to
support. In our previous discussion of how the UMLS represents
“Aspirin,” we noted that different formulations of aspirin
(aspirin, Aspergum, and Ecotrin) has been represented as distinct intensional
meanings in one of the sources (see Figure
5 As another example, the UMLS CUI “C0002871” groups the SNOMED
term Anemia, NOS# and
the ICD-9-CM term Anemia, unspecified together. On the surface, this
mapping appears to be quite reasonable. However, there is a problem that
occurs when we consider iron deficiency anemia, which is clearly a kind of
anemia. In ICD-9-CM, due to an explicit exclusion, iron deficiency anemia is
excluded from the category Anemia, unspecified. Therefore, SNOMED's
Anemia, NOS has a different intension than ICD-9-CM's Anemia,
unspecified in that it includes iron deficiency anemia but the ICD term
does not. Furthermore, if one mapped through the CUI from SNOMED to ICD-9-CM
(or vice versa), a semantic inaccuracy would be introduced that could be
undesirable in a medical record but might be beneficial in other settings (for
example, by improving query recall when trying to link concepts from medical
records to the medical literature). What, then, is the right perspective, or the right combination of
perspectives (to the extent that multiple perspectives can coexist), on
extensional meaning for the UMLS? We need to characterize more explicitly the
precise purposes for which the current Possible World of the UMLS is most
appropriate. Through such characterization, we can not only delineate the
proper perspectives for the UMLS but can also begin to ask questions about the
proper granularity of concept representation the UMLS and its source
terminologies should embody as well. Discussion In this paper, we have presented a framework for interpreting the semantics
of the UMLS, paying particular attention to the different senses of meaning
represented by the CUI and by the UMLS sources. We have tried to justify our
interpretation of the UMLS by analogy, through use of Ogden and Richard's
meaning triangle, and by demonstrating consistency with historical themes of
semantic interpretation. Others have discussed Ogden and Richard's meaning
triangle in the medical informatics
context,23,24,25,26,27,28
but none have used Ogden and Richard's framework as a direct aid for
understanding the semantics of the UMLS. In addition, we promote the notion
that the CUI is understandable only extensionally, by examining the
terms from the UMLS sources that are linked via a CUI. Through this linkage,
we argue that the CUI takes on extensional meaning—meaning that
is different from the intensional meaning represented by the UMLS
sources. This extensional interpretation of the UMLS—where we use a
Possible World framework as the source for a CUI's extensional set, rather
than the more typical corporeal world—is unique. An important
implication of assigning the CUI extensional meaning is the recognition that a
CUI's meaning changes any time a new term is included in—or an existing
term is removed from—the CUI's extensional set. This change in meaning
is not limited to identification of historical mistakes in the assignment of
source terms to CUIs, but rather is part of the natural evolution of the
semantics of the UMLS as new sources are integrated. Some readers may suggest the merits of assigning intensional meaning to the
CUI itself, in addition to its extensional meaning. In such a scenario, the
CUI would represent both a class of concepts (all the terms from sources
linked by a common CUI) and the extension of a higher order concept (a concept
that must somehow be inferred by examining the class). Others may argue that
such a scenario seems both incongruous and circular. As authors, we have not
resolved this debate, even among ourselves. Although we may debate the intensional and extensional characteristics that
we individually assign to the CUI—based on the characteristics that the
UMLS embodies today—the UMLS is an evolving artifact that may change in
ways that will force us to reconsider our interpretation. Debating these
intensional and extensional characteristics serves to highlight the ambiguity
of what the CUI is, and what it is intended to be. Within such debate we must
also consider the implications of various interpretations and use the
understanding thus attained to inform the evolution of the UMLS in ways we
collectively would consider optimal for the range of purposes for which the
UMLS is likely to be used. One implication of such debate is the need to consider the effects that
various interpretations and uses of the UMLS CUI will have on the
relationships among the National Library of Medicine, the UMLS source
providers, and vendors of terminology-enabled applications. There are
important accountability, resource, contractual, copyright, and intellectual
issues that must be considered. We hope that the UMLS framework will be
understood in a way that fosters collaboration between the National Library of
Medicine and the providers of the terminology systems it incorporates. With
such an understanding, vendors of terminology-enabled applications are more
likely to recognize synergistic value provided by both the UMLS and the source
terminologies it integrates. What direction will the relationships, accountability, and resource
commitments surrounding our terminologic needs ultimately take? Although we
cannot be certain, we certainly encourage an active debate. Through such
debate our understanding of the problems will improve and our ability to solve
those problems will be enhanced. Acknowledgments The authors thank Mark Tuttle, Stephanie Lipow, Alexa McCray, and John
Thomas for thoughtful discussions and advice regarding this manuscript. Notes This work was supported by training grant LM-07033 and resource grant
LM-05305 from the National Library of Medicine and by a medical informatics
postdoctoral fellowship from the Veterans Administration. Footnotes *We borrow the phrase “thoughts, words, and things” from the
title of the first chapter of Ogden and Richards' seminal book The Meaning
of Meaning,3
originally published in 1923. †Jaroslav Peregrin credits Carnap with replacing Frege's distinction between
Sinn and Bedeutung (Frege's original German words, which
have been translated as “sense” and “denotation”) with
the distinctions between intension and extension. ‡We do not seek in this article to prove formally the analogy between the
UMLS and Possible Worlds as used in modal propositional calculi. However, we
believe that the UMLS can readily fit into formal Possible World frameworks
such as described by
Stein,13 and that
such a framework may provide useful insights and perhaps functionality. §The UMLS contains propositions that state which terms are equivalent to one
another. Each such proposition thereby specifies the existence of a concept
and links that concept to a set of terms from the source terminologies that
are equivalent given a particular perspective represented by a Possible
World. The meaning of a term in the extensional sense is given just by listing, or
somehow indicating, what things are referred to by the term.¶For philosophers prior to Frege the extension of a concept was reserved for
only physical objects that share the essential characteristics of a concept.
Frege introduced the notion that the extension of a concept can also refer to
abstract concepts that share the essential characteristics of a concept. For
example, Frege used such extensional sets to represent a definition of the
“direction of line a” as the extension of the concept
“parallel to line
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[Medinfo. 1995]