=Paper=
{{Paper
|id=Vol-3637/paper5
|storemode=property
|title=Generics in Defeasible Reasoning: Exceptionality, Gradability and Content
Sensitivity
|pdfUrl=https://ceur-ws.org/Vol-3637/paper5.pdf
|volume=Vol-3637
|authors=Gabriele Sacco,Loris Bozzato,Oliver Kutz
|dblpUrl=https://dblp.org/rec/conf/jowo/SaccoBK23
}}
==Generics in Defeasible Reasoning: Exceptionality, Gradability and Content
Sensitivity==
https://ceur-ws.org/Vol-3637/paper5.pdf
Generics in Defeasible Reasoning: Exceptionality,
Gradability and Content Sensitivity
Gabriele Sacco1,2 , Loris Bozzato1 and Oliver Kutz2
1
Fondazione Bruno Kessler, Via Sommarive 18, 38123 Trento, Italy
2
Free University of Bozen-Bolzano, Piazza Domenicani 3, 39100, Bolzano, Italy
Abstract
The problem of representing defeasible information is a long-standing topic of discussion in Knowledge
Representation: for example, considering logic-based ontology representation languages, in Description
Logics many proposals for defining defeasibility and typicality have been formalised, mostly emerging
from existing approaches from the non-monotonic logic literature. On the other hand, little attention
has been devoted to study the capability of these approaches in capturing the interpretation of typicality
and exceptions from a formal ontological and cognitive point of view.
To address this, we here consider the notion of generics as discussed in the linguistic and cognitive
literature, i.e. a category of sentences about classes of individuals and admitting exceptions. We then use
our analysis as a possible guide for understanding the important features of defeasible information in
commonsense reasoning. In this paper we analyze different aspects of generics and we provide some
initial desiderata for formalizing defeasible reasoning in DLs.
Keywords
Generics, Defeasible Reasoning, Description Logics
1. Introduction
Representing and reasoning with defeasible information is a long-standing topic of discussion in
Artificial Intelligence (AI), dating back to the origins of the field of Knowledge Representation
(KR): in the presence of stronger conflicting information (or exceptions) with such defeasible
information, one wants to retract what we would have inferred in view of new information. In
its formalisation in different non-monotonic logics [1], this form of reasoning has been considered
since the earliest days of KR as one of the parts of the common-sense that artificial systems
should have to be considered actually intelligent [2, 3]. The classical example in the non-
monotonic logics literature is the Penguin example (see, e.g., [1]): if we know that Tweety is a
bird and we also know that birds fly, then we are willing to infer that Tweety flies. However,
if we come to know that Tweety is in fact a penguin and this makes us retract the previous
conclusion: we are more inclined to say that Tweety does not fly instead.
Considering logic-based ontology representation languages, in Description Logics (DLs) many
proposals for defining defeasibility and typicality have been formalised: as a matter of fact,
CAOS VII: Cognition and Ontologies, 9th Joint Ontology Workshops (JOWO 2023), co-located with FOIS 2023, 19-20 July,
2023, Sherbrooke, Québec, Canada.
$ gsacco@fbk.eu (G. Sacco); bozzato@fbk.eu (L. Bozzato); Oliver.Kutz@unibz.it (O. Kutz)
0000-0001-5613-5068 (G. Sacco); 0000-0003-1757-9859 (L. Bozzato); 0000-0003-1517-7354 (O. Kutz)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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most of them emerge from existing approaches in non-monotonic logics [4, 5]. On the other
hand, little attention has been devoted to study the capability of these approaches in capturing
the interpretation of typicality and exceptions from the point of view of formal ontology
and cognitive aspects. Thus, often a lack of discussion about the philosophical and cognitive
assumptions of this kind of reasoning is noted. Namely, when looking at non-monotonic
logic only as a tool, evaluating the systems with the sole criterion of evaluation to check the
functionality of the particular formal system proposed w.r.t. a particular reasoning problem, we
end up with a fragmented set of approaches. This, clearly, increases the difficulty to compare
and therefore properly evaluate comparatively such systems from a more general point of view.
Moreover, since in the end these tools should be used to model knowledge and reason in real
world scenarios, we also need criteria that allow us to decide if the ontological and cognitive
assumptions that the formal systems imply are justified or not. For these reasons, we are here
interested in discussing these foundational aspects of defeasible reasoning in DLs with the goal
of developing a DL system based on an ontologically and cognitively well-justified foundation.
A particularly interesting take on defeasibility, and defining our focus in this paper, comes
from the literature on generics [6, 7]. Generics are defined as sentences reporting a regularity
regarding particular facts that can be generalised even if they admit exceptions. In the penguin
example, for instance, the sentence “birds fly” can be considered a generic since it states
something about the individuals of the class “bird”, but still allowing exceptions like the members
of the sub-classes “penguins”, “ostriches” and “emus”.
Studying defeasible reasoning based on generics appears to be promising for a number of
reasons: first of all, according to [7], the central examples that are taken as reference points in
the literature on non-monotonic logic can all be considered as involving generics, and therefore
we can put forward the idea that other kinds of defeasible reasoning can all be traced back to
an account of generics; secondly, discussing generics allows to directly address the issue of
exceptions, which is a distinctive feature of both generics and defeasible reasoning [8, 9]; lastly,
it provides an excellent starting point to reflect on the ontological, metaphysical, and cognitive
assumptions explicitly or implicitly made by the various accounts of defeasible reasoning [10].
Consequently, the goal of this paper is to report on the works on generics with an ontological
and semantical lens and to extract some characteristics that are relevant for a comparison
of the existing approaches to non-monotonic logic. In particular, we provide the following
contributions: we analyse different aspects of generics (Sec. 2–4) and we provide some initial
desiderata for formalising defeasible reasoning in DLs (Sec. 5).
2. On Generics
First of all, let us give a more detailed presentation of generics. As said above, generics are
general propositions that admit exceptions [6]. Examples of generics found in the literature
include
1. “Lions have manes",
2. “Dogs have four legs" and
3. “Mosquitoes carry the West Nile virus".
As we can see from these examples, an intuitive way to formalise these sentences, the kind
of straightforward reading, suggests to consider them as universally quantified propositions.
However, under some further scrutiny, it becomes evident that they are not: in fact, we consider
them ‘globally true’ even if there are individuals in the class under consideration that do not
have the predicated property. In the cases above, exceptions could be (1) female or cub lions, (2)
unfortunate dogs that encountered some accident and lost a leg and (3) non-infected mosquitoes.
Therefore, when considering the sentences as universally quantified statements, such exceptions
would render them simply as false.
Some important observations have been made on generics in [6]. A first remark is that the
number of exceptions that the three generics above admit is different. In the first case, we can
imagine that the number of lions without a mane is probably more than 50% of all the existing
lions; in the second, exceptions would be just few individuals; in the third case, the exceptions
would be almost all the members of the class. We will discuss this in more detail below, but
this observation already suggests that generics can clearly not be treated as simple quantified
sentences.
A second important point is the difference between generics and direct kind predications [6].
Even if their form in natural language is essentially the same, the latter predicate a property
directly to the kind, whereas generics predicate a property to the individuals belonging to the
kind. For instance, sentences like “Dinosaurs are extinct” or “Dogs are widespread” are direct
kind predications. Thus, you can say that Bob the dog has four legs, following Example 2, but it
does not make sense to say that Bob the dog is widespread, being a direct kind predication.
These two initial observations show that not all the sentences that in natural language
have this general form are generics. In particular, this means that there are other kinds of
generalisations. However, as we have seen, the peculiar characteristic of generics is that they
tolerate exceptions, that is there are individuals that belong to the class and fail to have the
predicated property. Therefore, the question that needs to be tackled is in what semantical
sense generalisation can be true and at the same time admit exceptions.
This issue has been addressed mainly in two distinct fields: linguistics and cognitive psy-
chology [6, 8]. In the former, the focus has been on giving a semantics to generics in order to
model them formally; in the latter, the attention has been directed towards what generics can
say about our cognitive system of generalisation and therefore about concepts and kinds. Of
course, the two research interests are related and influence each other, however, it is important
to remember that they are different in both their goals and thus in their results. In the following
sections, we will briefly present some of the core research from both these fields and discuss
if and and in what way they may help with our goal of giving a theoretical and ontological
grounding to non-monotonic reasoning in KR languages.
2.1. Generics and Cognition
The main points of the analysis of generics from the perspective of cognitive psychology are
referred to by [6] as the generic-as-default hypothesis and sensitivity to content-based factors
[11, 8].
The generic-as-default hypothesis affirms that generic sentences correspond to the default
generalising mechanism of the mind, that is the fundamental one, from which the other systems
derive. This is very interesting and arguably counter-intuitive if we consider that from a
theoretical and logical point of view the standard generalisation is the universal one based on
the standard semantics. Moreover, as we will see, this will be in conflict with some semantic
approaches to generics, where generics are indeed reduced in some way to universal quantified
proposition.
The sensitivity to “content-based factors hypothesis” supposes that the generalisations made
by generics are sensible to elements related to what the generalisations are actually about. [8]
individuates these factors as:
“The counterinstances are negative, and:
If F lies along a characteristic dimension for the Ks, then some Ks are F, unless K is
an artifact or social kind, in which case F is the function or purpose of the kind K;
If 𝐹 is striking, then some Ks are F and the others are disposed to be F;
Otherwise, almost all Ks are F.” [8, p. 43]
The first factor is that the members of the kind that do not have the predicated property are
exceptions if they only lack the property, that is, if they do not also have an alternative property.
This makes these members exceptions, instead of counter-examples that falsify the statements.
For example, “Lions have manes” is true because the lions that fail to have a mane lack this
property and do not have something else in place of it.
The second factor corresponds to the observation that the acceptability of a generic depends
on “characteristic properties” of the kind. Examples of characteristic properties are peculiar
physical attributes, as for example manes for lions, or reproductive methods for animals, like
in the case of laying eggs for ducks. Similarly, with respect to artefacts or social kinds what is
relevant is whether the property corresponds to the function or the purpose of the kind. For
example an orange crushing machine should crush oranges, and this makes the proposition
“orange crushers crush oranges” true even for completely new orange crushers that never
crushed an orange.
The third factor is the poignancy of a property, as for example whether it is a deadly property.
This is the case for generics like “sharks attack bathers” and “mosquitoes carry the West Nile
virus”. However, it is relevant here to note that the individuals that do not have the property in
question have the disposition to have it, that is, they could potentially have it.
The last element is the more intuitive one, where most of individuals have the predicated
property. Examples are “tigers are striped” and “dogs have four legs”. This factor seems to
suggest that quantified propositions using most or equivalent adverbs of quantification are
closely related to generics. However, a precise discussion of this point is beyond the scope of
this paper, and we leave it for future research.
This cognitive analysis of generics is not directly connected with a specific formal charac-
terisation of generics, but it gives some insights on what should be taken into account in any
such formalisation. In particular, it also guides us in extracting some relevant elements for our
analysis of defeasible reasoning.
Regarding the first element, that is, the generic-as-default hypothesis, it is interesting because
it would suggest that from a cognitive point of view, defeasible reasoning is more basic and
foundational than classical deductive reasoning, a point also defended by [12]. In fact, generics
seem to be what actually introduces exceptions and therefore defeasibility in human reasoning:
if they are the natural mode of generalisation then also defeasible reasoning is the natural mode
of reasoning. This, for the moment, is only a conjecture that needs to be further investigated.
However, it seems to accord with the intuitions of the first generation of researchers in defeasible
reasoning, especially in the field of Artificial Intelligence. These researchers showed a strong
interest in this reasoning because they considered it the type of reasoning that is used in
everyday situations. Indeed, with the suggestion of [11], we can consider generics as judgements
corresponding to Kahneman and colleagues’ System 1.
2.2. Generics and Ontology
The second aspect, namely the sensitivity of generics to content-based factors, gives us some-
thing more concrete to discuss with respect to what can be elicited for a discussion of the
theoretical desiderata for defeasible reasoning. In fact, as [8, 11] calls them, the factors quoted
above are “worldly truth makers”. In other words, that list is the description of how the world
has to be to make a generic true. This means that they are not semantic conditions, but rather
ontological ones, because they explain how reality has to be, not how the language is related to
reality.
However, the content-dependency should not be completely overlooked. In fact, an impor-
tant observation that has been remarked in the literature about generics is that they are not
quantifiers, or not purely extensional, in the sense that they tell nothing about how many indi-
viduals are instances of the generalisation [11, 7, 9]. Consequently, we hold that in developing a
semantic for generics it is needed to refer to the content of the particular generic sentence.
A last interesting observation about these worldly truth conditions for generics, related to the
previous one, is that they are essentially conditions on the generalised property, rather than on
the individuals of the kind to which the property is predicated. That is, we cannot simply look
at the individuals instantiating or not the property, but we need to look at the property itself
and see if it is striking, for example. The only exception is the last point, which in fact is stated
as a classical quantified statement. In fact, even if the first point refers to “counterinstances”, it
actually says something about the property, namely if it has positive alternatives, as we have
seen in the case of the mane of the lions.
Now we can move on to the proposals of how to formalise generics: we first report on the
discussion of the syntax used for them and then illustrate and discuss some approaches used
for the semantics.
3. The Formalisation of Generics
3.1. The Syntax of Generics
In most presentations, the syntactic way of representing generics is quite uncontroversial and
it is inspired by the framework [13] developed for adverbs of quantification. It consists in
a tripartite structure of the form 𝑄[𝑅][𝑆], where 𝑄 corresponds to the quantifier, 𝑅 is the
restrictor, which sets the domain of 𝑄, and 𝑆 is the scope, which expresses the properties that
𝑄 𝑅𝑠 have.
Using the example in [6], we can represent the generic “Typhoons arise in this part of the Pacific"
as
𝐺𝑒𝑛 𝑥 [𝑇 𝑦𝑝ℎ𝑜𝑜𝑛(𝑥)][Arises-in-this-part-of-the-Pacific(𝑥)]
or as
𝐺𝑒𝑛 𝑠 [In-this-part-of-the-Pacific(𝑠)]∃𝑦[𝑇 𝑦𝑝ℎ𝑜𝑜𝑛(𝑦) ∧ Arises-in(𝑦, 𝑠)].
The former corresponds to the interpretation of the generic statements as “Typhoons in general
have a common origin in this part of the Pacific", whilst the latter corresponds to the alternative
interpretation “There arise typhoons in this part of the Pacific".
At this point, we need to remark that even if the logical syntax for generic statements is the
same as that for sentences with adverbs of quantification, the former cannot be reduced to the
latter. Actually, generic statements cannot be reduced to other quantified statements, for a
deeper argument see [11]. In fact, the main debated issue about generics is how to interpret
them semantically.
3.2. The Semantic Approaches to Generics
According to [6], we can recognise five main approaches in giving the semantics to generics.
Here, we will briefly address each of them in order to discuss if and eventually what they can
suggest about the theoretical grounding of defeasible reasoning.
3.2.1. Relevant Quantification
One way to try to explain the meaning of generics is by considering a generic as a universal
quantification only over relevant individuals. This makes 𝐺𝑒𝑛 in some way context-dependent,
since what is relevant should be determined by the context. The main problem of this approach
is that as it is, that is without criteria to decide what is a relevant individual, it can justify the
truth of any generic sentence.
For our purpose, this makes explicit the fact that we need to be able to decide over which
elements of the domain we are reasoning on. That is, we need to find a criterion that is able
to discriminate between the individuals we are considering and those outside of the scope.
Conversely, we can try to see this the other way around: trying to define the characteristics
according to which certain individuals are regarded as exceptional, i.e. those individuals which,
using the standard quantifiers, should satisfy the generic/inference, but actually do not.
3.2.2. Indexical Approach
Another approach is to consider 𝐺𝑒𝑛 not only context-dependent, but also indexical. That is,
what counts is not only the semantic context in which the generic is found, but also the context
of utterance. This means that what counts to determine the truth value of a generic includes
the intention of the person uttering it.
This approach has a similar problem to the previous one, because again this explanation seems
to be incomplete since it lacks clear criteria regarding what makes a specific generic true or
false.
The intuition of evaluating a generic according to its context of utterance does not seem helpful
for our goal. Since we are interested in using the analysis on generics to gain insights to use
in formalising defeasible reasoning, the context of utterance is something that could not be
easily considered. Rather, if there was strong evidence supporting this approach, it could be an
important objection to our purpose. However, since this is not the case, we will simply maintain
a careful eye on further developments from this direction.
3.2.3. Probabilities
The main proponent of this approach identified by [6] is Ariel Cohen, who suggests to understand
generics in a probabilistic way. In this approach, there are two main types of generics: absolute
generics and relative generics. We can use two examples to show what they are: an instance of
the first type is “Tigers are striped" and it can be paraphrased as “A randomly chosen tiger is more
likely to be striped than not"; an instance of the second type is instead “Mosquitoes carry the West
Nile virus", which can be understood as “In choosing a mosquito and another insect, it is more
likely that the mosquito carries the West Nile virus rather than the other insect". The difference,
as we can see in the examples, is that absolute generics refer to the probability of satisfying
the property among the individuals of the kind; whereas in the case of relative generics we
are considering also alternative kinds which could satisfy that property. Therefore, in the first
case the generic is absolute because we use a threshold that tells us if the probability is high
enough to make the generic true. While in the second case it is relative because we compare
two probabilities and we look at which of those is the greater one.
There are some counterexamples that strike at the very structure of this approach [6], however,
what seems to be the most relevant one for us is that for reasoning purposes it is simply not
very helpful. In fact, it seems that it would be very difficult to use this approach to reason on
individuals, since it does not tell us when a specific individual satisfies or does not satisfy the
generic.
Nonetheless, we found interesting the idea used in the case of relative generics of comparing
alternatives to the kind and the property to evaluate the generic. On one hand, it allows to
deal with complicated cases like that of mosquitoes carrying the West Nile virus, where the
individuals satisfying the generic are a minority; on the other hand, it allows to avoid to decide
arbitrarily a threshold to reach for the satisfaction of the generic.
3.2.4. Modal Interpretations and the Notion of Normality
Many researchers, with [7, 9] among them, rely on the possible worlds semantics to interpret
generics. The intuition is that generics say something about what normally holds for the
individuals of a kind, and so they refer to normal possible worlds to evaluate if a generic is
true or not. For example, possible worlds are ordered with respect to normality and a generic
statement is considered true if and only if it is true in the most normal worlds for the kind we
are considering [7].
According to [6], a shortcoming of these approaches is the fact that they do not seem to be able
to explain why generics like “Mosquitoes carry the West Nile virus” or like “Sharks attack bathers”
are accepted as true. In fact, it does not sound correct to interpret them as “Normally, mosquitoes
carry the West Nile virus” and “Normally, sharks attack bathers”. Difficulties arise also for the
interpretation of generics like “Ducks lay eggs”, since the solution proposed of restricting the
domain to the relevant sub-kind, in this case female ducks, gives rise to new problems and is
experimentally adverse.
A more fundamental issue is that the problem of explaining generics is not really solved, but
rather moved to the background. In fact, without a discussion and a definition of what ‘normally’
means we are essentially begging the question. Even if the definition of what is normal in each
application domain is left to the experts of that domain, if there is not a common definition
of normality available, this could easily lead to a fragmentation of the approaches, having a
different treatment of generics in each field. This would mean that generics are not actually
a unified phenomenon, but rather different phenomena that are explained differently in each
specific domain.
However, this approach gives us interesting elements to discuss for our purpose. Firstly, the
proponents of this account emphasise the fact that generics have an intensional character, since
they cannot be explained by a purely extensional approach. That is, they cannot be simply
treated as quantified sentences. According to [7] and [9], this is due to the normative connotation
of generics. This means that accidental generalisations are not generics. To be a generic there
should be a tie between what is meant by the subject and the property that is predicated. This is
why, for instance, there are generics that make sense and can be evaluated true or false even if
there are no instances of them. Examples taken from [7] include “This machine crushes oranges”
and “Kim handles the mail from Antarctica”. Both of them can be considered true even if the
machine has never been used for crushing oranges, because it is the machine’s function to
crush oranges, and because there is no mail from Antarctica, but that geographical area is Kim’s
responsibility. As we have seen, also [11, 8] agrees that generics cannot be treated as quantified
statements because they cannot have a purely extensional representation. Nevertheless, [11]
argues that referring to intensionality is still too coarse-grained. Consequently, we have to
refer to the actual content of the generic as we discussed above in the context of the content-
sensitivity factor.
Secondly, if discussed properly, normality could be an explicit criterion to look at to distinguish
what is relevant and what is not for the evaluation of the truth of generics. Moreover, discussing
normality would be interesting also because it allows to address the problem from the other way
around, that is, to discuss what are exceptions to a generic. A step in this direction has been
done, for instance, by [9]. Even if her aim is to account for the similarities and differences of
two linguistic variants of generics, the analysis is useful for more general purposes. Therefore,
further work on the analysis of this notion could be of great help in the understanding of
generics.
Thirdly, this approach is particularly relevant for us, since [7], who argued and discussed the
relation between generics and defeasible reasoning, endorse this approach. In fact, a classic
approach in non-monotonic logic, known as preferential or selection semantics [1], is very
similar to this way of understanding generics. Where the latter uses an order among possible
world, using normality as a criterion, the former uses an order among models, using normality
as a criterion too.
A last point that is interesting, but seems to be mostly overlooked, is the interpretation of
“normally” when used to paraphrase a generic. In fact, with a generic of the form “𝐾𝑠 𝜑𝑠”, can
be rephrased as “Normally, 𝐾𝑠 𝜑𝑠” or as “Normal 𝐾𝑠 𝜑𝑠”. The difference between the two
variants is substantial: in the first case, we are saying that what is normal is the state of affairs
corresponding to the statement; whereas, in the second case, we mean that we are speaking only
of normal instances. However, these interpretations may not be completely independent. For
example, one could argue that the general interpretation is the former, but that it corresponds
to the latter.
3.2.5. Prototypes
Researchers in prototype theory approaches often endorse a similar position. In fact, even if
they do not use the notion of normality, they affirm that generics should be interpreted as
statements about typical individuals. Using the example above, they would say that a generic
can be rephrased as “Typical 𝐾𝑠 𝜑𝑠”.
There are two main ways reported by [6] to understand the notion of typicality: the first is to
refer to a stereotype, the second to refer to a prototype. The distinction between the two is
not deeply discussed in the text, however it appears that the core difference is that stereotypes
emerge from culture, whereas prototypes are related to the cognitive sphere. Nonetheless, [6]
report an objection that they apply to both. The concern is that in this approach it seems that
for someone to hold a belief is regarded a sufficient condition to make it a true generic. However,
whilst we think that this can apply to the stereotype view, since, as we have said, stereotypes
emerge from cultural background and therefore they are not necessarily grounded in reality, it
does not easily apply to the prototype view. In fact, the latter approach is inspired by a theory
in cognitive science, which tries to describe what structure concepts have. Therefore, how the
prototype is actually built does not necessarily depend simply on the beliefs of people.
The account that we will propose can be considered as belonging to this general approach. In
fact, discussing briefly the prototype theory about concepts coming from the cognitive science
side will make evident its link to generics and therefore to defeasible reasoning.
4. The Prototype Theory About Concepts
According to the endorsers of the so-called prototype theory about concepts, to fall under a
concept does not mean to satisfy a precise definition, but rather to satisfy enough features or
constituents of that concept [14]. Another way of describing this account is to compare the
individuals and see if they are similar enough to fall under the same concept. Ideally, then, it
could be possible to have an individual which is the best example of that concept, that is the
prototype of that concept. However, it is better to think of the prototype as a more abstract
object, that is, as a “concept that was constituted from the different ways in which the category
members resembled each other and differed from nonmembers” [15, p. 80].
For instance, we classify Cluedo, tag, football and Pac-Man all as games, because each of them
satisfies enough features of the concept game. In fact, developing a definition of game which is
able to encompass all four of them is very complicated, to be generous, and even if we were
able to make one, finding an instance of game which would be left out would not be so difficult.
[15] individuates four phenomena about categories on which prototype theory relies: vagueness,
typicality, genericity and opacity.
• Vagueness is about the ‘boundaries’ of the concept, it means that it is not always clear
if an individual lies inside or outside the scope of the concept we are considering. For
example, it is not clear for the biologist if viruses should be considered living organisms
or not.
In the literature on generics, [9] relies on a similar idea of vagueness to account for
their exception tolerance mechanism. In this case, what is vague is which individuals
are actually considered as satisfying the generic. Therefore, this first property of the
prototype theory about concepts can be seen also in generics with small differences, at
least according to [9].
• Typicality means that the instances of a concept can be more or less ‘good’ examples of
that concept. For instance, lions are better examples of Carnivora than pandas.
Here, there is a link with generics, too. In fact, as we have seen, there are accounts
of generics that resort to typicality. However, here there is an important distinction
that could lead to a development of this kind of approach. In this case, typicality is a
graded notion, that is, you can compare different individuals and see which ones are more
typical instances of the concepts. The tendency in the literature on generics, instead, is
to use typicality in a Boolean way, so to say: either you are a typical instance, or you
are not. Trying to use the idea of typicality of the prototype theory could improve an
interpretation of generics by making it more flexible.
• Genericity is the phenomenon which actually corresponds to the formulation of what we
have called generics so far, that is, statements that seem to be about the entire class, but
that admit exceptions.
This is the most evident tie between generics and the prototype theory, which strongly
supports the attempt to take into consideration also this theory about the structure of
concepts for a formal account of generics and, therefore, for a formalisation of defeasible
reasoning.
• Opacity means that the criteria of categorisation are not clear to the one doing the cate-
gorisation. This is directly connected with the problem of formulating a precise definition
for the concept, in fact the case of games above is an example of this phenomenon: it is
not clear according to which criteria those games are games.
In a certain sense, we can state that this property can be found in generics, too, and it
is witnessed precisely by the difficulty of giving a semantic characterisation of them.
Basically, we can consider the struggle in developing approaches that represent and
maybe explain generics as a struggle to make this opacity a bit more transparent.
These four main properties show the deep connection of the prototype theory developed in the
cognitive research on the structure of concepts to the research on generics. Consequently, we
think that they can be usefully related to generics and therefore to defeasible reasoning.
5. The Desiderata for a Non-monotonic Logic Aware of Generics
So far we have discussed generics and the prototype theory of concepts. Now we can sum
up what emerged as a useful theoretical foundation and discussion for defeasible reasoning
approaches.
1. Exceptionality: this is actually more a general presupposition to the purpose. As we have
seen, we need a criterion that is able to discriminate and somehow explain when a generic
is true and when it is not. That is, which manages to distinguish the relevant individuals
from the irrelevant ones. Consequently, it should “recognise” when we have an exception
and when we do not. In terms of defeasible reasoning, it means that this criterion is able
to tell us when the inference applies and when it does not.
In the approaches discussed above, two of these criteria were normality and typicality.
But in the first case we do not have a proper theory of normality, and so this is not
an effective solution. Whereas, in the case of typicality, we can take advantage of the
prototype theory of concepts, developed in cognitive science, to have a more precise
notion of this criterion.
2. Gradability: as we have seen in the case of relative generics in the probabilistic approach
and in the definition of typicality in the case of the prototype theory for concepts, it could,
and we think it is, useful to apply a relative or comparative approach, rather than an
absolute one. This is more in line also with the vagueness that characterises prototype
theory, since we do not have a clear boundary that allows us to say this lays inside and
this outside, conversely we need to compare the elements and decide if they are similar
enough to fall in the same class. This means, in the case of typicality for example, that
instead of typical individuals and atypical ones of some concept, we have more or less
typical individuals.
3. Content sensitivity: an important point that emerged at different times during the above
discussion is the irreducibility of generics to a purely extensional explanation. Their
content sensitive character has been understood mainly in two different ways: in terms
of a semantics that resorts to possible worlds and the notion of normality, or alternatively
as a semantics that resorts to relations among concepts, as in the case of the prototype
approach. This last interpretation is more in line with the property of content-sensitivity
formulated in the analysis of generics from the point of view of cognitive psychology.
6. Conclusions
In this paper we provided an overview on generics and discussed the ways in which they can
be of use for giving a principled foundation to non-monotonic reasoning methods. We derived
three desiderata from this discussion, exceptionality, gradability, and content sensitivity.
A wider discussion on the relationship between generics and the literature on non-monotonic
reasoning from the point of view of cognitive science and philosophy is still needed in order
to further complete the discussion on the theoretical foundations of defeasible reasoning and
for a complete review of the existing approaches in DLs. For example, [11] observes that
inferences involving generics are not “formal", meaning that they depend on the particular
generic considered. Moreover, [6] affirm that the main assumption of the non-monotonic
reasoning literature seems to be reflected in the experiments: that is, normally, the property
predicated by an accepted generic is also attributed to an arbitrary exemplar of the kind involved
in the generic; however, it is observed that the literature considers only non-troublesome cases
corresponding to high-prevalence generics.
A full technical development of our account, however, is also needed in order to verify the
feasibility from a formal and computational point of view and to provide a precise comparison
with existing approaches (see [16] for an initial proposal). Finally, it would be interesting to
perform an evaluation of the desiderata we identified from a cognitive point of view.
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