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Definitional Foundations for Intelligent Systems, Part II: Constructing a Definition and Examples

Authors:

Abstract

We posit that the lack of consensus definitions of (machine or artificial) intelligence might be affected by the lack of knowledge of conceptual analysis and other well-investigated theories. Acute contextualization of the concepts that are defined may also be an issue. Accordingly, in this two-part paper, we review some basic concepts from across research fields on how to explicate a definition. In Part I we propose 30 quality criteria for definitions that shall serve as guidelines for well-defined definitions of any concept. The quality criteria may allow for both better insights into definitions and a wider understanding of the current discourse on AI. In Part II we provide basic terminology on definitions and an iterative process to guide the construction of robust definitions by considering the quality criteria introduced in Part I. Our central goal is twofold: we want to facilitate understanding across fields and inform different stakeholders from industry, academia, legal and governments, among others, by contributing to the formal foundations on elucidating "good and robust definitions" for AI.
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Definitional Foundations for Intelligent Systems,
Part II: Constructing a Definition and Examples
Dagmar Monett1 and Colin W. P. Lewis2
1 Computer Science Dept., Berlin School of Economics and Law, Germany, and AGISI.org
2 AGISI.org
1 dagmar.monett@agisi.org, 2 colin.lewis@agisi.org
Abstract
We posit that the lack of consensus definitions of (machine or artificial) intelligence might be
affected by the lack of knowledge of conceptual analysis and other well-investigated theories.
Acute contextualization of the concepts that are defined may also be an issue. Accordingly, in
this two-part paper, we review some basic concepts from across research fields on how to
explicate a definition. In Part I we propose 30 quality criteria for definitions that shall serve as
guidelines for well-defined definitions of any concept. The quality criteria may allow for both
better insights into definitions and a wider understanding of the current discourse on AI. In Part
II we provide basic terminology on definitions and an iterative process to guide the construction
of robust definitions by considering the quality criteria introduced in Part I. Our central goal is
twofold: we want to facilitate understanding across fields and inform different stakeholders
from industry, academia, legal and governments, among others, by contributing to the formal
foundations on elucidating “good and robust definitions” for AI.
Keywords: Artificial Intelligence, definitions, intelligence, quality criteria
Main Conference Topic: Robotization, Engineering and Artificial Intelligence
Introduction
Well-defined definitions are essential in any field. They are seen as a condition for
progress [6], help to guide research [15, 21], and show the way towards a clear target [4] or
goal of the field. However, established theories and practices that deal with the definition of
concepts are rarely considered by most practitioners. For example, a thorough conceptual
analysis of intelligence or of the concepts intelligence is based or depends on, has been
unfortunately missing in the AI community. Kelley in The Art of Reasoning [10] suggests that
a definition and the concept we define through it should provide a neutral framework for
thought and discussion “so that people on opposite sides of an issue can rely on a common
understanding of the relevant concepts in presenting their arguments and thus understand each
other.” Consequently, he states that “it is not a good idea to include controversial information
in a definition.” This is not the only desired property of a good definition, though. Several other
desirable properties or quality criteria for definitions were introduced in Part I of this paper.
There, we also introduced the problem of not having an overarching definitions of artificial
intelligence (AI) and why this has been a stumbling block in the development of the AI field.
In Part II, we introduce basic terminology on definitions as well as an iterative process for
constructing a definition. We also provide examples to clarify some of the quality criteria
introduced in Part I of the paper.
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Basic Terminology on Definitions
In this section we first introduce the basic terminology on definitions, like the
constituents of a definition, its types and purpose, among other related subjects. The section’s
aim is to raise awareness of the importance of these subjects, long overlooked by most
stakeholders although essential to the definitional foundations of any field.
What is a Definition?
A definition “states a thing’s essence,” it “expresses the nature of a thing and its
substance.” These were Aristotle’s words in his Posterior Analytics [1] written in 350 B.C.E.
Since then, a myriad of definitions of what a definition is has been proposed, but almost all of
them converge to the same idea: the purpose of a definition is to state, express, explain, or
specify what a thing is. According to the Cambridge Dictionary, a definition is not only “a
statement that explains the meaning of a word or phrase,” i.e. its essence, its substance, but
also “a description of the features and limits of something,” i.e. its characteristics and scope.
Definitions can be defined by expressing the meaning of the thing to be defined in very different
ways: there are definitions that do it by using other constructs where the meaning is known;
these are the lexical definitions when concepts from a lexicon or dictionary are used. Ostensive
definitions exemplify things to which the expression applies because examples are pointed out.
And stipulative definitions express the meaning by proposing how the language should be used.
These three broad categories, lexical, ostensive, and stipulative definitions, have received
different designations with time and have been subdivided into further subcategories.
How Should a Definition be Defined?
Definitions enable people to understand a concept or theory; thus, providing conceptual
clarity on how definitions should be defined is, although mostly overlooked, an essential
activity prior to the use of the concept or theory. According to Cassidy [3] after his analysis of
several Aristotelian works on definitions, a concept may have many definitions and how it is
defined “is a function of the language in which it is stated,” i.e. “the way we talk about things
is a function of the things we talk about.” Furthermore, a definition is a “verbal formulae of
selectively grouped data taken from the knower’s experience” [3]. Hence, there is no unique
way of defining a concept, definitions may be inherently contextual, and they would depend
on both the people that define them and their area of knowledge.
A definition should have the form of “an equivalence” [20], of “a two-part equivalence”
[18], which on the one hand contains the thing to be defined, the definiendum, and on the other
hand the expression that defines it, the definiens. Ideally, the definiens follows the definiendum
in order of appearance and both are constructed in such a way that certain Rules of Definitions
[10, 20] are fulfilled. The definiendum, for example, should be a short, grammatically simple
expression that specifies the concept that is being defined. Similarly, the definiens should fulfill
certain rules that guarantee, for example, that the concepts used in its expression have a
meaning that is previously known or that has already been defined: “[i]t may be a sentential
function of an arbitrary structure, but containing only those constants whose meaning is
understood; that is, the meaning of each of those constants either is immediately obvious or
has already been explained” [20]. Furthermore, it should not be too broad or too narrow,
circular, nor use negative terms unnecessarily, ambiguity or vagueness, nor obscure or
metaphorical language [10].
In his empirical work on Logic, Mercier [14] states that to define “is to say what a thing
is.” One way of stating the meaning of the definiendum is by referring to its genus and
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differentia as part of the definiens, like in Aristotelian definitions. The genus or kind is the
broader category the definiendum belongs to. For example, in Gottfredson’s definition
“Intelligence is a very general mental capability that [...] involves the ability to reason, plan,
solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from
experience” [7], mental capability is the genus of intelligence, i.e. the broader concept. The
differentia, however, distinguishes the concept from other definienda, in that it specifies the
properties or characteristics that differentiate the definiendum from other concepts from the
same genus, as it is expressed in the rest of Gottfredson’s example.
A definition could have different functions and be “relative to various purposes” [22].
It can clarify the boundaries of a concept, the relationships among concepts, and it can also
provide a summary statement about the referents of a concept, i.e. it can highlight its essence
[1, 10]. According to Kelley [10], “[a] good definition condenses the knowledge we have about
the referents of a concept, giving us just the highlights, the key points, the essence.”
Conceptual Analysis
One of the main activities philosophers deal with is conceptual analysis. As pointed out
by Aaron Sloman [19], conceptual analysis is “required for improving our understanding not
of the physical world itself, but of how people of various ages and cultures think about the
world.” On the other hand, our understanding of the world builds on certain assumptions
without it would not be possible to construct or define most common concepts we know [5].
When we define a concept, we fix it, we isolate it from the rest [22], thus how we define it
matters. According to [13], conceptual analysis “specifies a set of conditions that are
individually necessary and jointly sufficient for the application of [a] concept.” As such,
conceptual analysis encompasses a series of strategies and methods that seek to analyze and
describe concepts, phenomena, and theories. Some of these strategies are extensively detailed
in [19] and summarized in what follows. They may be a necessary step that must be considered
before constructing a definition of a concept, in parallel to the process of defining it, or even
after doing that, for instance when a definition must be refined or improved to cope with
advances in a particular field of study. Some strategies presented in [19] for analyzing a given
concept are:1
Collecting descriptions of both varied instances and non-instances of the concept, and
comparing them. This would help to clarify the specificity with which the concept is or
should be defined.
Criticizing and extending already existent definitions, e.g. definitions given in
dictionaries or by other practitioners in the field. A thorough revision of the literature
should avoid unnecessary re-definitions of an already defined terminology.
Collecting examples of the concept and related words that may illustrate one concept but
not the others; also collecting examples of their use and how to teach the concept to other
people. This might help to understand the concept and its definition by others, as it will
be discussed later in this paper.
Asking what the role of the concept is in a given culture or context, which should its
purpose be, whether it would guide research in a given field and how. This could
determine the type of the definition and the way it is constructed.
1 We refer the reader to the cited work for a detailed description of these and other strategies.
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Listing ways in which the truth or falsity of statements involving the concept in question
can be tested. This may allow for the conceptual clarity to which a good definition ought
to contribute.
How to Construct a Good Definition?
The Rules of Definitions [10, 20] introduced above consider a set of properties that a
definition should meet in order to be considered a good definition. Kelley [10] argues, for
example, that if a definition includes a genus and a differentia that are both not too broad and
not too narrow, and that state the essential attributes of the concept referents, then it is quite
probable that it will also satisfy other rules from the set he proposes which is comprised by six
rules altogether. One way of searching for such a combination of genus and differentia, which
is the classic way to define a concept, is by following Plato’s method of definition known as
Diairesis or method of division, developed in [17] and later refined by Aristotle in his Posterior
Analytics [1]. The idea is that a definition should include all essential elements that make it
both exclusive and comprehensive (see quality criteria 14 and 15 from the list presented in Part
I of this paper) by successively considering the similarities and distinctive properties of these
elements with regard to other instances of the same category, thereby avoiding both the
omission of important characteristics and the inclusion of others that are not essential to the
definition. This way of constructing a definition is consistent with the first three rules of
definitions presented in [10] and commented at the beginning of this section. However, they
are not the only criteria that are desirable for having a good definition, as we have already
discussed in Part I of this paper. In addition to this, there is no unique way of defining a concept
(see a compendium in [5]). We suggest to construct a definition as part of an iterative process.
The one presented in what follows extends the process presented in [10], in that many more
quality criteria are included and a few of them are strengthened after considering the results
discussed here and in [16]. Our iterative process is depicted in Figure 1. Such an iterative
process could be preceded by a systematic conceptual analysis as suggested in section about
conceptual analysis. It consists of the following steps:2
(i) Use a two-part equivalence to set the form of the definition: define the definiendum as
short and simple as possible (for example, start the definition with “Intelligence is ...”).
Define the definiens with a genus-differentia expression that states the “what,” the “how,”
and the “why” of the concept that is being defined (see quality criteria 1 to 4 from Part I
of this paper) as short and simple as possible. In particular, once the genus or broader
category is found, “choose a differentia that distinguishes [the concept] from other
concepts in the same genus [i.e. which is the genus of transparency and which other
concepts belong to the same category?]. If there is more than one distinguishing
attribute, choose the most essential one,” as suggested in [10], because it would be easier
to explain what makes that attribute special, distinguishable from the rest. A previous
conceptual analysis may shed light in this endeavor.
(ii) State the differentia in an ostensive way (see the section on basic terminology, as well as
quality criterion number 5 from Part I of this paper). For example, when defining the
concept of human agency, include capabilities or functions that indicate agency (i.e.
exemplify the “what” in order to understand it better). Do not make the definition too
ostensive nor too narrow, however.
2 The Defintly App, available at http://defintly.com and with provisional password agisiorg, contains most of
the content presented in this two-part paper and assists users when defining concepts in any field.
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(iii) Go through the list of quality criteria for definitions (see Part I of this paper) and evaluate
whether each of them fits the functions of the definition (see section on basic terminology
above) and in which context and extent.
(iv) Add (resp. remove) content to (resp. from) the definiens to meet the quality criteria. Seek
for simplicity but sought for as many fulfilled quality criteria as possible.
(v) Adapt the wording and remove unnecessary expressions.
(vi) Iterate the steps i) to v) as long as it is needed. In particular, take a look at the language
and use it elegantly, thereby ensuring that the already-met quality criteria are still
fulfilled, i.e. that they are not violated by occasionally changing the language.
(vii) Stop the process when no more improvements are necessary.
Figure 1: Iterative process to construct a definition
Constructing a definition that satisfies all quality criteria might not be possible. Even
keeping all of them in mind when following the iterative process might not be straightforward
at the beginning. With time and practice, however, it would be more intuitive and simpler to
define concepts that follow these principles. The advantages in doing so would be considerably
positive. Each and every person involved would benefit from a well-defined definition: not
only the author(s) of the definition but also the reader(s) and people that use it. Hence, both the
community and the scientific discourse would profit likewise and advance further, because it
would be easier to discard less expressive definitions and, thus, easier to reach consensus.
Examples
The only purpose of this section is to exemplify which quality criteria from the list
presented in Part I of this paper are met or not by a definition. It is not in the scope of this paper
to construct a new definition of intelligence, since it would require at least an added, extensive
analysis of the several already existent definitions of intelligence from the literature (refer to
[11] for a compendium) as already discussed in the section on conceptual analysis. Instead, a
selection of examples of new, suggested definitions from the survey presented in [16] are
presented below. Their most relevant characteristics are analyzed and discussed.
“Intelligence is the ability to do the right thing at the right time given a dynamic
environment (that is, a shifting landscape of `right times’ requiring more `right things’).
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[Artificial Intelligence] is intelligence constructed deliberately as an artefact of a
culture.” Joanna Bryson, University of Bath and University of Princeton
Bryson’s definition defines the “what” of the definition and it makes an explicit
distinction between human and artificial intelligence. It is not ostensive (i.e. it doesn’t include
examples), but it could be considered operational since it exemplifies “how” to reach
intelligence, i.e. by “[doing] the right thing.” This definition is short, affirmative, and general.
If separated from the whole, the second part of the definition would contain a vicious circle.
“To my mind, intelligence (whether we’re speaking of a human or a machine) is the
ability to put one’s finger on the essence of situations that one faces, and to do so
reasonably rapidly. Or a bit more verbosely, … ‘intelligence is the art of rapid and
reliable gist-finding, crux-spotting, bull’s-eye hitting, nub-striking, essence-pinpointing.
It is the art of, when one is facing a new situation, swiftly and surely homing in on an
insightful precedent (or family of precedents) stored in the recesses of one’s memory.
That, no more and no less, is what it means to isolate the crux of a new situation. And
this is nothing but the ability to find close analogues, which is to say, the ability to come
up with strong and useful analogies.’” Douglas Hofstadter, Indiana University, also
citing [9]
Hofstadter’s definition defines the “what” and is ostensive: it exemplifies cognitive
abilities that indicate intelligence. It also defines the “how” and includes examples of
behavioral functions to reach intelligence, thus it is operational. It is not a short definition, but
it is affirmative, comprehensive, and useful. Furthermore, it is an intellectually elegant
definition. However, it might not be a clear definition for some audiences. Finally, let’s analyze
some definitions from the literature:
“Intelligence is a very general mental capability that, among other things, involves the
ability to reason, plan, solve problems, think abstractly, comprehend complex ideas,
learn quickly and learn from experience. It is not merely book learning, a narrow
academic skill, or test-taking smarts. Rather it reflects a broader and deeper capability
for comprehending our surroundings -- `catching on,’ `making sense’ of things, or
`figuring out’ what to do.” [7]
Gottfredson’s definition, which was already used as an example in the section on basic
terminology above, was the most agreed upon definition of intelligence in [16]. Of the 567
people that participated in the survey,3 a total of 356 respondents agreed (38.1%) or strongly
agreed (24.7%) with this definition, representing about two-thirds of positive agreement. It is
also a widely accepted definition among experts in intelligence and allied fields [8], such as
neuroscientists and psychologists. Linda Gottfredson is a psychologist. It should be mentioned
that more than 70% of all participants in the survey are computer scientists, engineers,
mathematicians, and physicists. Is Gottfredson’s definition a good definition of intelligence?
One of its most distinguishing characteristics is that it exemplifies several cognitive abilities
when defining the “what,” i.e. when defining intelligence. In fact, it was the most ostensive
definition from the survey, which presented a total of 18 definitions of intelligence from the
literature to agree upon. It can be verified that it fulfills almost all 30 but three quality criteria
(no. 17, 18, and 30). This is very interesting since other definitions explicitly avoid the
3 The AGISI survey was closed in July 2019. The results included here are considered to be final. Partial results
are presented in [16].
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specification or exemplification of capabilities and are therefore considered more abstract and
general by their authors, thus better for defining intelligence. That is the case of Legg and
Hutter’s definition of machine intelligence [12]: “Intelligence measures an agent’s ability to
achieve goals in a wide range of environments.” The authors analyze several examples of
definitions in detail and claim that intelligence is the effect of capacities and not the result of
having a set of them. Legg and Hutter mostly refer to semantic aspects, i.e. to which extent and
how the analyzed definitions define intelligence or not, thereby justifying why their own
proposed definition of intelligence might be more appropriate. Furthermore, they argue that it
is very difficult to specify the capacities that might be needed and that they would depend on
the concrete context at hand. It seems contextual definitions are too specific for some authors.
However, ostensive definitions are more preferred by researchers and practitioners: Legg and
Hutter’s definition had only a 48.7% of total positive agreement from the respondents to the
survey (276 respondents agreed (37.4%) or strongly agreed (11.3%) with that definition) and
it was ranked fourth place overall. Other definitions, Gottfredson’s included, were much more
favorably ranked by respondents. A commonality is that they are ostensive.
If we look back at the examples presented in this section, not all of them follow the
Aristotelian construct. Moreover, not only one genus but different genera were used by the
authors to define the broader category intelligence may belong to. Which of them is the most
appropriate level of abstraction might be in itself a very controversial topic. Ideally, a good
definition satisfies many of the 30 quality criteria for definitions presented in Part I of this
paper.
Conclusion
Part II of this paper introduced definitional foundations for definitions. These included a
process for constructing good definitions of concepts, from scratch, in particular, the concept
of intelligence. Examples were also provided to illustrate some of the quality criteria that were
introduced in Part I. We do not recommend a technical perspective for the analysis of these
topics; our wish would be the AI community being more knowledgeable about what other non-
technical disciplines have considered so far. A similar analysis as the one presented here for
the concept of intelligence could be applied to the definition of those concepts that are having
a crucial role in establishing the guidelines and foundations for AI. We hope our work can
contribute to informing different stakeholders from industry, academia, legal and governments,
among others, on how to do such an analysis.
Acknowledgment
We would like to thank Aaron Sloman for his enlightening suggestions about conceptual
analysis and its relation to definitions.
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References
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https://blogs.lse.ac.uk/polis/2019/11/18/new-powers-new-responsibilities/.
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[4] Chollet, F. (2019). The measure of intelligence. arXiv:1911.01547 [cs.AI].
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[13] Margolis, E., & Laurence, S. (2019). Concepts. The Stanford Encyclopedia of
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[22] Watts, A. W. (1951). The Wisdom of Insecurity: A message for an age of anxiety. Second
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Brief biographies of the authors
Dagmar Monett
Prof. Dr. Computer Science (Artificial Intelligence, Software Engineering) with 30+
years of research and teaching experience. Co-founder of the AGI Sentinel Initiative,
AGISI.org, dedicated to understanding intelligence in order to build beneficial AI and to
educate society’s stakeholders across disciplines. AI expert at Ms.AI, “Artificial Intelligence
for and with Women.”
Colin W. P. Lewis
Adjunct Professor and international business and policy advisor, specialized in the
social and economic impact of technological change. With specific knowledge of the evolving
conditions of technology for productivity growth, development, labor, (in)equality, and
competitiveness. Part of his work focuses on understanding human intelligence and creating
solutions for Artificial Intelligence.
ResearchGate has not been able to resolve any citations for this publication.
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