Annotation with adpositional argumentation: Guidelines for building a Gold Standard Corpus of argumentative discourse

Abstract

This paper explains Adpositional Argumentation (AdArg), a new method
for annotating arguments expressed in natural language. In describing this
method, it provides the guidelines for designing a Gold Standard
Corpus (GSC) of argumentative discourse in terms of so-called
argumentative adpositional trees (arg-adtrees). The theoretical
starting points of AdArg draw on the combination of the linguistic
representation framework of Constructive Adpositional Grammars
(CxAdGrams) with the argument categorisation
framework of the Periodic Table of Arguments (PTA). After an explanation of these two
frameworks, it is shown how AdArg can be used for annotating
arguments expressed in natural language. This is done by providing
the arg-adtrees of four concrete examples of arguments, which substantiate the
four basic argument forms distinguished in the PTA. The present
exposition of the fundamental tenets of AdArg enables the building
of a GSC of argumentative discourse, that means an
annotated corpus of texts and discussions of
undisputable high-quality according to argumentation theory
experts. Such a GSC should be conveniently annotated in terms of
arg-adtrees, which is a time-consuming process, as it needs highly
skilled annotators and human supervision. However, its role is
crucial for developing instruments for computer-assisted
argumentation analysis and eventual application based on machine
learning natural language processing algorithms.

Full text

Annotation with Adpositional Argumentation
Federico Gobbo∗& Marco Benini & Jean H.M. Wagemans
11 October 2019
Preprint
How to cite
Gobbo, Federico; Benini, Marco; Wagemans, Jean H. M. 2019. Annotation with
Adpositional Argumentation: Guidelines for building a Gold Standard Corpus of
argumentative discourse. Intelligenza Articiale, vol. 13, no. 2, pp. 155-172.
DOI
10.3233/IA-190028
Abstract
This paper explains Adpositional Argumentation (AdArg), a new method for an-
notating arguments expressed in natural language. In describing this method, it
provides the guidelines for designing a Gold Standard Corpus (GSC) of argumenta-
tive discourse in terms of so-called argumentative adpositional trees (arg-adtrees).
The theoretical starting points of AdArg draw on the combination of the linguistic
representation framework of Constructive Adpositional Grammars (CxAdGrams)
with the argument categorisation framework of the Periodic Table of Arguments
(PTA). After an explanation of these two frameworks, it is shown how AdArg
can be used for annotating arguments expressed in natural language. This is
done by providing the arg-adtrees of four concrete examples of arguments, which
substantiate the four basic argument forms distinguished in the PTA. The present
exposition of the fundamental tenets of AdArg enables the building of a GSC of
argumentative discourse, that means an annotated corpus of texts and discussions
of undisputable high-quality according to argumentation theory experts. Such a
GSC should be conveniently annotated in terms of arg-adtrees, which is a time-
consuming process, as it needs highly skilled annotators and human supervision.
However, its role is crucial for developing instruments for computer-assisted ar-
gumentation analysis and eventual application based on machine learning natural
language processing algorithms.
Keywords: computational argumentation; natural language processing; gold standard
corpora; argumentation theory; rhetoric
∗Corresponding author. E-mail: F.Gobbo@uva.nl.

1 Introduction
Over the last decade, Computational Argumentation has emerged as an independent
eld of research. One of the core challenges within this eld is to develop methods
for representing argumentative texts and discussions so as to enable their analysis
and evaluation. So far, researchers have developed various computational models
of argument that are used, for example, in developing tools for argument mapping,
argument mining and computer-aided human decision making—for a representative
collection of recent work within this eld, see Modgil et al [21].
One would expect researchers within the eld of Computational Argumentation to
draw on insights from the long-standing elds of Argumentation Theory and Rhetoric,
which have produced a great many theories about the way in which people support
their points of view with arguments. These linguistic and pragmatic theories pertain
to the nature and constituents of various types of arguments, the structure of dierent
genres of argumentative discourse, as well as the stylistic features of such discourse.
In combination with normative standards regarding the validity, reasonableness, and
eectiveness of argumentation, this knowledge is used for providing theoretically
informed analyses and evaluations of argumentative texts and discussions—for a
comprehensive survey, see van Eemeren et al [8].
So far, however, researchers in the elds of Articial Intelligence in general and
Computational Argumentation in particular have used only a small part of the in-
sights generated within Argumentation Theory and Rhetoric. Since these insights
are expressed in informal terms, they are not easily transferred in operative models
suitable for computation—for a historical overview of argumentation models in AI
related settings, see Bench-Capon and Dunne [3].
An important characteristic of current computational models of argument is that
most—if not all—of them operate on the abstract level of complete propositions and
the interactions between them, without taking into account the detailed linguistic and
pragmatic information contained in these propositions. This goes, for example, for
approaches inspired on Dung’s abstract argumentation frameworks [
6
], which study
sets of atomic arguments and their interrelations.
It also applies to approaches that take Walton’s argument schemes [
32
] as a point
of departure, in which an argument scheme is taken to consist of a conclusion and a
set of premises—see, e.g., Dondio and Longo [
7
]. However, in reality rarely premises
are independent, hence they do not form a set. For example, if n is a natural number
(rst premise), and it is even (second premise), then the remainder of the division of it
by 2 is 0 (conclusion). In this case, to make sense of the conclusion and of the second
premise, the rst premise is strictly needed.
Another example is given by approaches based on the Toulmin model [
26
]. They
are able to provide a detailed description of the techniques for monological and dia-
logical structure of arguments and the resolution of the conicts (via semantics), as
described in Longo’s ve-layers model [
16
],[
17
], with a practical application in Rizzo
and Longo [
22
]. Although the Toulmin model, apart from conclusion and premises,
does contain linguistic elements that are relevant for analyzing and evaluating ar-
gumentation, it only covers a small part of the linguistic and pragmatic richness of
arguments expressed in natural language. As an immediate consequence, the process of

reconstruction of arguments should be performed before applying Longo’s ve-layers
model.
In relation to the approaches just mentioned, we argue that the linguistic and
pragmatic analysis should be performed in advance, that is, before treating arguments
in a purely non-linguistic, abstract, formal way. As a result, the very notion of what is
an argument will be claried and expressed in terms that satisfy both researchers in
Articial Intelligence and in Argumentation Theory.
In this paper, we explain Adpositional Argumentation (AdArg), a high-precision
method for representing arguments expressed in natural language. While partially
based on Gobbo and Wagemans [
12
,
13
], the main aim of this paper is to show how the
method can be employed for the purpose of building a GSC of argumentative discourse.
This means that we shall rene, extend, adapt, and illustrate the theoretical framework
of AdArg as it is explained in earlier papers. It is important to underline that AdArg
does not contradict the abovementioned approaches. Rather, it enables the formal
modeling of argumentative discourse on a dierent level of abstraction, namely, on the
level of the natural language in which arguments are expressed. This means that our
work may be used as input for approaches such as the ones mentioned above, which
model argumentation on a non-linguistic, more abstract level.
The paper is structured as follows. In Section 2, we give a brief example of argument
reconstruction, illustrating four requirements we think are important for reaching
a high level of inter-annotator agreement. In Section 3, we explain the theoretical
framework of the Periodic Table of Arguments (PTA). We focus on its compliance with
the rst requirement of enabling a normalization of natural arguments. By including
analyses of examples of such arguments that instantiate all four basic argument forms
distinguished in the PTA, we also illustrate its compliance with the second requirement
of being a comprehensive yet exible categorisation of argument. Then, in Section 4, we
briey decribe the mathematical foundations of Constructive Adpositional Grammars
(CxAdGrams) as well as the characteristics of its central notion of ‘adpositional tree’.
We then show in Section 5 how to combine CxAdGrams and the PTA into AdArg,
demonstrating the compliance of our argument representation method with annotation
requirements three and four. In the conclusion of the paper, Section 6, we reect on
remaining issues in relation to the further improvement and implementation of the
guidelines for building a Gold Standard Corpus (GSC) of argumentative discourse.
2 Argument reconstruction
A recent annotation of a debate between Clinton and Trump [
2
] gives an example of a
natural argument that can be reconstructed as consisting of two propositions, one of
which functioning as the conclusion and the other as the premise. This is the original
text:
(largest banks in America) are much bigger than they were when we bailed
them out for being too big to fail, we have got to break them up.
On the level of complete propositions, this text can be reconstructed as follows:

(conclusion) We should break up the largest banks in America.
(premise) They are much bigger than they were when we bailed them out
for being too big to fail.
Now, in order to analyze such arguments in more detail, and also to subsequently
evaluate their quality, the human analyst disposes of an extensive set of tools developed
in the eld of Argumentation Theory and Rhetoric such as those for explicitizing
implicit premises, analyzing the quality of warrants, and asking critical questions
associated with argument schemes. Unfortunately, a great many of these methods
and techniques have not yet been formalized in computational terms because they are
based on linguistic and pragmatic information that is more ne-grained than the level
of propositions and their interrelations.
Another problem that occurs when a single argument is reconstructed in terms of
premise and conclusion, is that there is a risk that dierent analysts—who can also
be annotators of a corpus of argumentative texts—reconstruct the same argument
in dierent ways, or even, worse, in incompatible ways. They might, for instance,
interpret the argumentative force in dierent ways, because of the ambiguity of natural
language or dierences in their subjective level of knowledge about argumentation
theoretical concepts or rhetorical techniques.
In our view, a high level of inter-annotator agreement could be achieved by re-
specting the following requirements. First of all, the annotation of argumentative
discourse should take place by using a controlled language format, that is, a normal
form, expressed in terms of a clear step-by-step procedure with explicit constraints
for the formulation of both premise(s) and conclusion. Second, this procedure should
enable the analyst to classify properly the arguments by the means of a taxonomy that
is comprehensive because it covers all possible arguments as identied in the tradition
of Argumentation Theory—and at the same time exible, so to be robust to the incom-
ing data. Third, it should permit the analyst not only to identify the meaningful parts
of the natural language material, but also to eventually hide non-necessary linguistic
details. Fourth and last, the method for representing arguments should represent the
linguistic and pragmatic information that is relevant for the analysis and evaluation of
arguments in an adequate way and be formal(izable) to the extent that it can be used
for the purpose of building tools that automatize these tasks.
3 The Periodic Table of Arguments
The Periodic Table of Arguments (PTA) is a formal linguistic categorisation of argument
types developed by Wagemans [
31
]. The PTA systematizes the traditional multitude
of incomplete, informal—and sometimes even inconsistent—taxonomies of argument
into a systematic and comprehensive whole, reducting ambiguity in the analysis and
therefore highening inter-annotator agreement. Below, we explain assumptions and
constituents of the PTA’s theoretical framework for the purposes of designing AdArg.
In the PTA and henceforth in AdArg, an argument is a building block of persuasive
discourse. Within such a building block, it is always possible to nd one or more
premises, indicated by the Greek letter
π
—standing for the Greek equivalent
πρότασις
(protasis)—and one and one only conclusion, indicated by the Greek letter
σ
—standing

for the Greek equivalent
συµπέρασµα
(sumperasma). Conclusions and premises can
be conceived as statements, that means it is always possible to express
π
and
σ
by
means of propositions, consisting of at least a subject (closely following a convention
common in Logic, indicated as a,b, etc.) and a predicate (analogously: X,Y, etc.).
A minimal argument consists of two statements, a conclusion
σ
and a premise
π
. For the purposes of this paper, we will give examples of minimal arguments only.
Linguistically, connectors between a conclusion and a premise in a minimal argument
present themselves in two complementary types: progressive and retrogressive—for
details see van Eemeren and Snoeck Henkemans [
9
, p. 33]. The progressive form
presents at rst the premise
π
and then the conclusion
σ
. In English, the connector
typically takes the form of ‘so’, but also ‘therefore’, ‘thus’, or other forms, are possible.
The analyst should be trained in recognizing all these forms as progressive connectors.
Conversely, the retrogressive form presents at rst the conclusion
σ
and then the
premise
π
. The typical retrogressive connector in English is ‘because’, but, again,
others are possible. For the sake of simplicity, in this paper we will give only examples
of concrete arguments with the retrogressive connector ‘because’. For more details on
the linguistic representation, see the next section.
Within the theoretical framework of the PTA, an argument is conceptualized as
a combination of two statements: a conclusion, which is doubted, and a premise,
which is (more) certain. An arguer who supports a conclusion with a premise can be
assumed to aim for rendering that conclusion (more) acceptable for the addressee. In
order to explain how this leverage of acceptability from the premise to the conclusion
works, the PTA approach assumes the ‘law of the common term’—see Wagemans [
28
].
This law states that the premise, in order to fulll the pragmatic aim of rendering
the conclusion (more) acceptable, should share exactly one common term with the
conclusion. While this common term can be characterised as the ‘fulcrum’ of the
leverage of acceptability taking place within the argument, the relationship between
the non-common terms, which expresses the underlying mechanism of the argument,
functions as its ‘lever’.
The law of the common term yields two basic possibilities of argument forms. If
the common term is the subject of the two statements, the argument has the form ‘
a
is
X
, because
a
is
Y
’. In this case, the subject (
a
) functions as the fulcrum and the
relationship between the predicates (
X
and
Y
) as the lever of the argument. For this
reason, such arguments are called ‘predicate arguments’ (pre).
If the common term is the predicate, the argument has the form ‘
a
is
X
, because
b
is
X
’. In this case, the predicate (
X
) is the fulcrum and the leverage of acceptability
can be explained by assuming that there is some kind of relationship between the
non-common terms of the premise and the conclusion, namely their subjects (Xand
Y
). Within the framework of the PTA, such arguments are called ‘subject arguments’
(sub).
The theoretical framework of the table is based on three partial characterisations
of an argument. We have just explained the rst characterisation, which entails the
distinction between predicate (pre) and subject (sub) arguments.
The second characterisation is based on there being two possible ways of expressing
statements that have an argumentative function: as a proposition or as an assertion—
see Wagemans [
28
]. The dierence between the two is that in the latter, the epistemic

commitment of the arguer regarding the acceptability of the statement is explicitly
present in the discourse. The statement
We only use 10% of our brain
, for example, is
expressed as a proposition, while the statement
It is true that we only use 10% of our
brain is expressed as an assertion.
Within the framework of the PTA, the distinction between propositions and as-
sertions is used to characterize arguments as ‘rst-order’ (1) or ‘second-order’ (2).
In normalizing rst-order arguments, the analyst can work with statements that are
expressed as propositions. But for second-order arguments, the normalization takes
place on the level of assertions. This means that if the epistemic commitment to the
acceptability of the statement is not present in the actual discourse, the analyst may
have to add a conventional expression of this commitment, ‘is true’ (
>
), as the predi-
cate of the conclusion and/or the premise of the argument in order to comply with
the law of the common term. In combination with the distinction between predicate
and subject arguments, this yields two additional argument forms: ‘
q
is
>
, because
q
is
Z
’, which is called a second-order predicate argument and has the proposition
q
functioning as the fulcrum and the relation between
>
and
Z
as its lever, and ‘
q
is
>
,
because
r
is
>
’, which is called a second-order subject argument and has the epistemic
commitment marker
>
as the fulcrum and the relation between propositions
q
and
r
as its lever.
The notions of ‘argument form’, ‘fulcrum’ and ‘lever’ can be illustrated by means
of an argument diagram. For the sake of simplicity, we will do this for the rst-order
predicate and subject arguments, which are situated in the Alpha Quadrant (
α
) and
the Beta Quadrant (β) of the PTA respectively—see Table 1.
Table 1: Overview of rst-order argument forms
quadrant conclusion premise retrogressive argument
(progressive variant)
α a is X a is Y a is X, because ais Y
(ais Y, so ais X)
β a is X b is X a is X, because bis X
(bis X, so ais X)
Figure 1 shows the argument diagram of rst-order predicate arguments. In this
type of argument, the conclusion ‘
a
is
X
’ (
σ
) is supported by the premise ‘
a
is
Y
’ (
π
).
The direction of the arrows towards the fulcrum (in this case, the subject
a
) means
that two dierent properties (in this case, the predicates
X
and
Y
) are ascribed to the
same subject. The relation
R
between these properties, the lever of the argument, is
marked as α, so to indicate the appropriate quadrant of the PTA.
Figure 2 illustrates the situation in the case of rst-order subject arguments, where
the fulcrum is the predicate (
X
), which means that the conclusion ‘
a
is
X
’ (
σ
) is
supported by the premise ‘
b
is
X
’ (
π
). The lever of this type of argument is the
relationship between the dierent subjects (aand b).
As said above, the theoretical framework of the PTA takes the conclusion and the
premise of an argument to be expressed by statements. The third characterisation of
arguments that constitues this framework is the argument substance, i.e., the specic

aX
Y
σ
π
α
Figure 1: Argument diagram of a rst-order predicate argument
b
aX
σ
π
β
Figure 2: Argument diagram of a rst-order subject argument
combination of types of statements. This is determined on the basis of a tripartite
typology that distinguishes between statements of fact (
F
), statements of value (
V
), and
statements of policy (
P
)—see [
31
]. An argument can thus be said to substantiate one of
nine possible dierent combinations of types of statements, conventionally put in the
order
σπ
:
PP
,
PV
,
PF
,
VP
,
VV
,
VF
,
FP
,
FV
,
FF
.
The government should invest in jobs, because
this will lead to economic growth
, for instance, can be characterized as a
PF
argument,
since its combines a statement of policy (
P
) in its conclusion
σ
—expressed in the
normal form before the retrogressive connector
because
—with a statement of fact (
F
)
in its premise
π
. For other examples of these types and statements and instructions on
how to distinguish them, please refer to the Argument Type Identication Procedure.
1
In order to help the human user of the PTA, conventional colors were added across
the four quadrants, indicating the combination of the types of statements instantiated
by the argument.
2
The color scheme is based on the idea of representing statements
of policy, value and fact by means of the primary color triad red, yellow and blue
respectively. As a result, combinations of types of statements are represented by these
primary colors if they are of the same type, and by the appropriate secondary colors
if they are dierent. An argument that has statement of policy as its conclusion and
a statement of fact as its premise, for instance, is represented by means of the color
purple, because that is the secondary color obtained by mixing red (policy) and blue
(fact). For typographic reasons, the colors of the PTA will not be represented here.
Readers can refer to Table 2 for the correspondences between the combinations of
types of statements and their conventional colors.
In sum, each argument should be classied as (1) a rst-order or second-order
1
J.H.M. Wagemans, Argument Type Identication Procedure (ATIP), Published
online January 28, 2019,
http://periodic-table- of-arguments.org/
argument-type- identification-procedure.
2
See the ocial web site: J.H.M. Wagemans, Periodic Table of Arguments: The building blocks of persua-
sive discourse. Published online December 9, 2017,
http://periodic-table- of-arguments.
org.

Table 2: Conventional colors of the argument types
Values (σπ) Conventional color
PP red
VV yellow
FF blue
PV, VP orange
PF, FP purple
VF, FV green
Table 3: Overview of argument types (PTA version 2.4)
quadrant argument form existing types
α1 pre FF, VF, VV, PV
β1 sub FF, VV, PF, PP
γ2 sub VF, VV, PF
δ2 pre VF, VV, PF, PV, PP
argument; (2) a predicate or subject argument; and nally, (3) as one out of nine
possible combinations of types of statements. The superposition of these three partial
characterisations, taken together, yields a factorial typology of argument that can be
used in order to develop tools for analysing, evaluating, and generating arguments in
natural language. The theoretical framework of the PTA distinguishes between four
dierent ‘argument forms’, a notion that comprises the rst two partial characteristics
mentioned above. In the visual representation of the PTA, the argument types instan-
tiating these forms are situated in four dierent quadrants, which are indicated with
letters
α
,
β
,
γ
, and
δ
respectively. Within each quadrant, arguments are further dier-
entiated depending on the specic combination of types of statements—see Table 3.
For each of the types of argument characterised in this way, the reconstruction of the
natural language material (even in combination with visual aids) is done in the normal
forms that leads to the formulation of a specic element present in the PTA.
When taken together, the three partial characterizations of argument constitute a
theoretical framework that allows for
2×2×9 = 36
systematic types of arguments.
However, not all possible combination in theory are found in practice. For instance, in
the Alpha Quadrant there is no
PP
element, while in the Beta Quadrant there is no
VF
element—see subsections 3.1 and 3.2 for details. On the other hand, there can be more
than one element corresponding to an argument type, depending on the linguistic
formulation of the lever, i.e., the relation between the non-common terms of the premise
and the conclusion. Each element representing the abovementioned systematic types
of argument may host a number of ‘isotopes’, which are named in accordance with
the existing dialectical and rhetorical traditions of argument classication. In the
following, we will present the argument types that are situated within each quadrant
of the PTA and describe their main characteristics.3
3
For a gure of the PTA version 2.4 as a whole and other examples analysed in detail, see the ocial web
site of the PTA: J.H.M. Wagemans, Periodic Table of Arguments: The building blocks of persuasive discourse.

3.1 The Alpha Quadrant
The Alpha Quadrant of the PTA comprises all the rst-order predicate arguments. Let
us introduce them via a concrete linguistic instantiation, to which we will refer from
now on as Example 1:
The suspect was driving fast, because he left a long trace of rubber
on the road
. This argument is to be identied as a rst-order predicate argument (
1
pre
) since it has the form ’
a
is
X
, because
a
is
Y
’ with the subject
a
as the fulcrum.
In fact, both linguistic subjects,
he
and
The suspect
, point to the same referent. Such
anaphora resolution can be performed by the analyst, possibly assisted by tools of
computational linguistics, although anaphora resolution is a well-known NLP hard
problem [19]. More details about the linguistic analysis are in Section 4.
After determining that the right quadrant for this argument is alpha, we can pass
to the analysis of the single statements. In particular, example 1 combines a statement
of fact (
F
) in the conclusion
σ
,
The suspect was driving fast
, with another statement
of fact (
F
) in the premise
π
,
he left a long trace of rubber on the road
. The systematic
name of this argument is therefore 1 pre FF.
Within every quadrant, the horizontal placing of the type of argument is determined
by the specic combination of types of statements that it instantiates (
FF
,
VF
,
PF
, etc.),
while the various isotopes, which reect the linguistic variations in the formulation of
the lever and relate the PTA to the traditional names of argument types, are placed in
a vertical line. Readers are invited to think about the history of Mendeleev’s Periodic
Table of Elements, upon which the PTA is inspired: not all elements were found in
the same moments, but there were some empty spaces left, as such chemical elements
were theoretically possible; analogously, the PTA contains spaces for theoretically
possible argumentative elements which have not (yet) been found.
In consulting the PTA (see Figures 3 to 6), the analyst (eventually with the assistance
of an expert system or another type of ad hoc software) quickly realises that there are
four isotopes of the systematic name 1 pre FF: Sig, Cau, Ef, Cor.
6
-
Sig
from
sign
Cau
from
cause
Ef
from
eect
Cor
from
correlation
1 pre FF
Cr
from
criterion
1 pre VF
St
from
standard
Ax
axiologic
argument
1 pre VV
Pr
pragmatic
argument
1 pre PF
De
deontic
argument
Ev
from
evaluation
1 pre PV 1 pre PP
Figure 3: The Alpha Quadrant of the PTA
Given that in our example, the relation between the premise and the conclusion
Published online December 9, 2017, http://periodic-table- of-arguments.org.

can be captured by saying that the predicate of the statement expressed in the premise,
leaving a long trace of rubber on the road
, is an ‘eect’ for the predicate of the conclusion,
driving fast
, the most suitable candidate for providing a traditional name of this specic
isotope of 1 pre FF is ‘argument from eect’.
We argue that this crucial step can be semi-automatized thanks to the linguistic
analysis in terms of argumentative adpositional trees (arg-adtrees). Section 4 will
illustrate in detail the procedure, using example 1.
3.2 The Beta Quadrant
The Alpha and Beta Quadrants contain the rst-order arguments, which are con-
ventionally situated on the positive side of the vertical axis of the Cartesian space
representing the PTA. In particular, the Beta Quadrant is adjacent to the Alpha Quad-
rant on the left (Figures 3 and 4). The beta quadrant represents all and only rst order
subject arguments. Figure 4 shows that the empty elements,
1 sub VF
and
1 sub PV
,
are situated in dierent spots then those of the Alpha Quadrant.
With the exception of the argument type with the systematic name
1 sub PP
, in
the Beta Quadrant every systematic type has isotopes. In order to illustrate the Beta
Quadrant, we will introduce another concrete instantiation, which we call for simplicity
example 2. The linguistic formulation of this example is the result of the reconstruction
of an explanation of legal reasoning—see Kolb [
15
]. In particular, it states:
Cycling on
the grass is forbidden, because walking on the grass is forbidden.
In this case, it is obviously the predicate
is forbidden (X)
that functions as the
fulcrum, while the subjects
a
and
b
are dierent. The argument thus follows the form
’ais X, because bis X’ and can be identied as a subject argument. Both conclusion
σ
and premise
π
are statements of value
V
, therefore the systematic name of the
argument type is 1 sub VV.
6

Sim
from
similarity
G
from
genus
Exa
from
example
Cas
case
to case
1 sub FF1 sub VF
An
from
analogy
Ma
a maiore
Mi
a minore
1 sub VV
Eq
from
equality
Pa
from
parallel
1 sub PF1 sub PV
Comp
from
comparison
1 sub PP
Figure 4: The Beta Quadrant of the PTA
Three ‘isotopes’ are possible: from analogy (An),
a maiore
(Ma) and
a minore
(Mi). Both
a maiore
(Ma) and
a minore
(Mi) argument types entails an asymmetric
comparison, that is, the respective values
V
of conclusion
σ
and premise
π
are not

on the same level, while the argument from analogy (An) does not show a particular
asymmetry. Thus, the analyst will classify example 2 as an instance of the argument
from analogy (An)—see Figure 4. A detailed explanation of the linguistic aspects of
example 2 is found in Section 4.
3.3 Second-order arguments and the Gamma Quadrant
After having discussed these examples of rst-order arguments, we now turn to the
second-order ones. In general, these arguments come in the same two forms as their
rst-order counterparts, depending on which term is the common term and thus
functions as the fulcrum: second-order subject arguments have the predicate as the
common term and second-order predicate arguments the subject. The dierence with
rst-order arguments is that the analyst, in order to identify the type of argument,
adds the epistemic commitment to the truth or acceptability of the conclusion (or
both the conclusion and the premise) to the statements. As we explained earlier, this
means that the argument is analysed on the level of the assertion instead of that of the
proposition.
Table 4: Overview of second-order argument forms
quadrant conclusion premise retrogressive argument
(progressive variant)
γ q is >ris >qis >, because ris >
(ris >, so qis >)
δ q is >qis Z q is >, because qis Z
(qis Z, so qis >)
The epistemic commitment is added in the form of its conventional expression ‘is
true’ (
>
). In particular, while in the Gamma !uadrant this expression functions as the
fulcrum, in the case of arguments situated in the Delta Quadrant the addition of
>
concerns only the conclusion (
σ
). In Table 4, we provide an overview of the resulting
argument forms.
Unlike rst-order arguments, the argumentative force of second-order arguments
does not particularly rely on the object level, that is, the inner structure of the proposi-
tions but on the meta-level, that means its semantic and pragmatic information. In
fact, the fulcrum, which expresses the epistemic commitment of the arguer, cannot
be found inside the inner traits of the argument but on the truthiness at the assertion
level.
After this general explanation of the nature of second-order arguments, we start
our discussion of conrete examples with the Gamma Quadrant, which entails all
second-order subject arguments. Let us consider the argument
War is bad (σ) because
peace is good (π)
. Both
σ
and
π
are statements of value, so the systematic name of this
argument, which from now on we will call example 3, is 2 sub VV.
It is worth noting, that, on the object level, neither the subject
a
of
σ
(
War
) and
the subject
b
of
π
(
peace
) coincide, nor the predicates
X
(
is bad
) and
Y
(
is good
). In
example 3, there is a clear opposition, that relies on the semantic information: it is


?
2 sub FF
T
from
tradition
1 sub VF
O
from
opposites
Di
from
disjunction
Pe
petitio
principii
2 sub VV
Con
from
consistency
2 sub PF2 sub PV2 sub PP
Figure 5: The Gamma Quadrant of the PTA
pretty straightforward that the pairs ‘war/peace’ and ‘bad/good’ are antonyms. For
this reason, within the three ‘isotopes’ (Figure 5) example 3 is identied by the analyst
as an argument from opposites (O).
The peculiarity of the Gamma Quadrant is that on the level of the propositions
themselves no fulcrum is found. For this reason, this quadrant can be called the
receptaculum ignorantiae
, as the argumentative force is found elsewhere. In fact,
neither semantic nor structural information (see Section 4 for the latter) suces to nd
the fulcrum, which is implicit. Thus, a level of abstraction should be added, in order to
nd the fulcrum. We call this level of abstraction the layer of epistemic information.
While rst-order arguments can bring particular intentional states, such intentional
states do not act as the fulcrum. For instance, in example 1 both the conclusion and
the premise can be considered committments, in terms of intentional states:
>
(I am
telling you that)
The suspect was driving fast because he left a long trace on the road
.
However, since this pragmatic information is not crucial for the identication of the
type of argument, such epistemic information is taken into consideration only in the
case of second-order arguments.
For instance, example 3 is made by two statements of values expressing beliefs,
that can be reconstructed like this: ‘you should believe that
σ
because you already
believe
π
’ (in symbols:
>VV
). It is such intentional state that represents the fulcrum
of example 3, and therefore its argumentative force—for more details, see Chapter 6 in
[
10
]. If specications are not needed, the umbrella predicate ‘is true’ (symbol:
>
) is
conventionally adopted.
3.4 The Delta Quadrant
Figure 6 shows the types of arguments within the Delta Quadrant of the PTA found
until now, up to version 2.4.
4
Let us introduce example 4, from the reconstruction of
a quite famous meme:
We only use 10% of our brain, because it is said by Einstein
. The
fulcrum here is to be found in the subject, which it is a full statement, ‘we only use
10% of our brain’ and ‘it’, represented by
q
. Clearly, if the statement in full is only the
subject, we need to add a second-order predicate, that in rst approximation will be ‘is
4
See also the ocial web site: J.H.M. Wagemans, Periodic Table of Arguments: The building blocks of
persuasive discourse, http://periodic-table-of-arguments.org.

-
?
2 pre FF
Au
from
authority
Po
ad
populum
Comm
from com-
mittment
2 pre VF
U
from
utility
Be
from
beauty
2 pre VV
Ba
ad
baculum
Car
ad
carotam
2 pre PF
Ch
from
character
H
ad
honorem
Eth
ethotic
argument
2 pre PV
Em
from
emotion
2 sub PP
Figure 6: The Delta Quadrant of the PTA
true’ (
>
). The reconstruction will be transformed as follows:
We only use 10% of our
brain
(
q
) [is true (
>
)], because
q
is said by Einstein (
Z
). On a more sophisticated level
of analysis of the epistemic information hidden behind the
>
, we could say that the
rst statement is one of speaker belief’s, hence it can be reconstructed as ‘I believe
that q’.
4 Constructive Adpositional Grammars
In this section, we shall demonstrate how the theoretical framework of CxAdGrams
can be applied to the types of argument situated in the four quadrants of the PTA.
More in particular, we will provide an analysis of examples 1–4. However, before
to to delve into the topic, a legitimate question can be raised: why should we care
of a ne-grained analysis of the linguistic material underlying the arguments? In
other words, why is an identication of the type of argument in terms of the PTA not
enough?
The answer of this question is twofold. The rst answer is general. The method
of reconstructing arguments we are illustrating should operate on the level of the
individual words, in order to help the analyst in the reconstruction itself. Our aim is to
go beyond the pure subjectivity in reconstruction, and the identication of a heuristic—
if not a step-by-step procedure—cannot avoid linguistic analysis. Our hypothesis is
that the application of CxAdGrams to the task of argument reconstruction can be
treated as a supervised machine learning problem, as outcomes are predicted on the
base of the data provided, analogously to the task of automatic summarization—see at
least Nenkova and McKeow [20].
The second answer is more specic. While the argumentative and pragmatic
information is language-independent to a large extent, the concrete arguments largely
depends on the natural language in use. Figure 7 illustrates the detailed levels of
abstraction within a single argument.
These levels can be identied as points of attack. On the upmost level (
arg
),
the argument itself can be attacked as a whole, through critical questions against
the solidity of the whole architecture. This in practice means that the attacker will
question the solidity of the ‘because’ (in case of retrogressive arguments: symbol
←
)

arg
σ
p-is->
txt
p
txt
π
p-is-Z
txt
p-is->
txt
p
txt
Figure 7: Levels of abstraction within arguments
or of the‘so’ (progressive:
→
), or other natural language connectors. Other levels of
attack are on the propositional level, that is the level of the premise(s) (
π
), and that of
the connection between the premise and the conclusion, that of the ‘argumentative
lever’ – see Section 3 above. These two levels could be managed nicely with the only
use of the PTA. However, attacks can arrive at the level of the epistemic information
(p-is-
>
; e.g. ‘I do not share your belief’), in case of second-order arguments—or, more
in general, on the level of the statement—an attack can question the solidity of the
statement being a fact (
F
; e.g. ‘
p
is fake’), values (
V
; e.g. ‘I have dierent values’),
and policy (
P
; e.g. ‘this policy is not feasible’). Quite often, such attacks focus on a
particular linguistic element (
txt
, in Figure 7) of the argument. This is the the specic
reason why we need a linguistic representation of arguments.
We can add a practical reason for a linguistic representation. In an argumentative
discourse, the vast majority of statements are arguments; however, it is possible to nd
expressive statements that are functional for argumentations but are not arguments,
such as Shakespeare’s Mark Anthony speech incipit:
Friends, Romans, countrymen,
lend me your ears
. In the Gold Standard Corpus (GSC) to be made, such statements
should be represented in terms of pragmatic adtrees—for details, see Chapter 6 of
Gobbo and Benini [10].
In the following section, we will present the fundamentals of CxAdGrams for the
purposes of the Adpositional Argumentation (AdArg), while in the next sections we
will analyse examples 1–4 in terms of argumentative adpositional trees (arg-adtrees).
4.1 Mathematical foundations
Constructive Adpositional Grammars
(from now on, CxAdGrams) in all their variations—
so far, morphosyntactic, argumentative, pragmatic, but phonological are also possible—
are based on a simple mathematical method, described in the Appendix B of the
fundamental book Gobbo and Benini [
10
]. Interested readers can look there for a
comprehensive presentation; here, we will convey only the necessary information for
the scope of the present paper.
Constructive mathematics is an approach to mathematics that is premised on
the idea that regarding the formulas of a theorem, the information content of any
statement should be strictly preserved—see Bridges and Richman [
4
]. This is established
by avoiding the use of the Law of Excluded Middle, unlike classic logic. Mathematical

representations of natural language grammars following the constructive approach
are well known in mathematical and computational linguistics, the rst ones being
proposed by Adjukiewicz [1] and Church [5].
In CxAdGrams, a
grammar category
is a category [
18
] enriched with grammar
characters (
gc
) and a set of basic constructions, essentially capturing the notions of
valency (
val
), and the adjunctive (
A
) and circumstantial (
E
) relations. An
adtree
is a
syntethic and syntactic description of the objects of a grammar category, which takes
the graphical form of a tree, apt to be easily presented, analysed and manipulated.
However, the notion of adtree is inadequate to represent the real constructions inside
languages, apart the most basic and elementary ones. For this reason, CxAdGrams
introduce the notion of transformation; mathematically, transformations are in fact
maps of a grammar category into itself which preserve the structure of grammar
categories—an
endofunctor
[
18
]; see Chapter 4 of Gobbo and Benini [
10
]; this aspect is
out of the scope of the present paper.
Using category theory to model AdGrams is justied because it allows to inherit
for free a number of mathematical notions and constructions which have a funda-
mental meaning in the analysis of a language. For example, the formal notions of
sieve
and
co-sieve
on an object (expression)
E
correspond to the collection of the
valid subexpressions of
E
and to the collection of all the expressions containing
E
,
respectively.
While this way of formally identifying the sub- and the super-pieces of an expres-
sion is useful in the mathematical analysis of linguistics, it becomes really essential
when using AdGrams to model the natural language for other purposes, such as AdArg.
In fact, identifying expressions in a coherent way, that is, if an expression is considered
to be equivalent to another expression then we can always substitute the rst expres-
sion with the second one in the fragment of the language under analysis, corresponds
to imposing a
Grothendieck topology
over the considered fragment, which naturally
generates a topos of sheaves. This abstract, complex, and very rich mathematical object
represents in an explicit way the information the fragment conveys by the structure
of the language alone.
However, since a topos of sheaves can be fully described in term of brations,
it becomes possible to computationally manipulate this abstract entity. In fact, a
convenient way to write brations is given by Homotopy Type Theory [
27
], in which
a bration is represented by a dependent product, or, in logical terms, by a bounded
universal quantication.
Avoiding the complex mathematical descriptions, the fragment collecting all the
expressions of interest, even identifying some of them as soon as the identication
makes mathematical sense, can be synthetically described in a formal language, the one
of Homotopy Type Theory [
27
], which is, at the same time, a functional programming
language, a logical theory powerful enough to analyse the properties of the fragment,
and a topological description of how the expressions in the fragment are related one
with the others.

4
dep
gc



q
↔
adp
gc
@@
@
4
gov
gc
4
children
O1



q
←

I2
1
@@
@
play
I2
Figure 8: The abstract adtree structure and example 0
4.2 Syntactic adpositional trees
From a linguistic point of view, adtrees represent natural language expressions in terms
of recursive trees, in which the relations between linguistic elements can be described
as hierarchical in that the one element ‘governs’ the other (which then ‘depends’ on
the former). Each adtree represents a minimal pair of linguistic elements and their
relation, expressed in terms of adpositions. Figure 8 (left) shows the abstract adtree
structure. The governing element (
gov
) is conventionally put on the right leaf at the
bottom of the rightmost branch, while conversely the dependent element (
dep
) is put
on the left leaf at the bottom of the leftmost branch. Immediately thereunder one can
nd the grammar characters (
gc
). Finally, the adposition (
adp
), which represents the
relation between the governor and the dependent, is depicted as a hook under the
bifurcation of the two branches.
On the right there is the syntactic adtree of example 0
children play
: we say
‘syntactic’ as the morphological analysis of
children
is hidden under the triangle
4
.
In general, the triangles on the leaves indicate the possibility of recursion, the fact
that another adtree can be appended to each adtree leaf recursively, if needed. This
possibility illustrates the fact that the analyst can hide or show details through the use of
triangles, according to her needs. The comparison between the abstract and the concret
adtree in Figure 8 helps the reader to understand the roles of each and every element:
the left arrow
←
indicates an unmarked information prominence, as the default is that
the governor (in example 0,
play
) is more prominent than the dependent (in this case,
children
). In arg-adtrees, the unmarked information prominence correspond to the
progressive form (see Section 3). The left-right arrow
↔
indicates underspecication.
By convention, non-morphological adpositions are indicated by Greek letters: in the
case of a syntactic relation, the letter is an epsilon (

); in the case of an argument, it
will be one of the letters for the quadrants (
α
,
β
,
γ
,
δ
), or
π
and
σ
for indicating the
argumentative function of the statements.
Finally, from a formal point of view, adtrees can be seen as formulas, which means
that they are suitable for natural language processing. The tabular presentation of
Figure 9 corresponds to the syntactic adtree example 0 in Figure 8.
Under the adpositions and the governor and dependent leaves readers can nd the
grammar characters (gc): in example 0, they are respectively: I2
1,I2,O1.
Table 5 shows the possible grammar characters (
gc
). Adjective (
A
) and circumstan-
tials (
E
) are both modiers, and for this reason in general they appear as dependents
(
dep
). It is worth noting that the left and right branches of a linguistic adtrees follow

←
I2
1
4(children)O1
playI2
Figure 9: The tabular adtree of example 0
Table 5: Linguistic grammar characters
Value Name Function Examples
A adjunctive modier of O adjectives, articles
E circumstantial modier of I adverbs, adverbial
expressions
I verbant valency ruler verbs, interjections
O stative actants nouns, pronouns
name-entities
U underspecied transferer prepositions,
conjunctions,
derivational
morphemes
dierent rules of construction: while governors (
gov
, right branches) can have more
dependents, dependents (dep left branches) can have one and one only governor.5
Each proposition is analysed in terms of phrases, which are depicted as subtrees;
each phrase presenting a ruling verb is built around that verb, which is posed as the
rightmost leaf of the respective subtree. The variable
gc
will take the value of I
val
act
in
the case of verbs. A valency value (
val
) is assigned to each verb on the basis of its use
in terms of constructions and it is expressed by an apex. Each valency value is fullled
by its dependent subtree, expressed in terms of a denite actant value (
act
), a nominal
expression (e.g. noun, pronoun) that fulls the semantic role described by the valency
value itself. Actant values are expressed by pedices both in verbs (I
val
act
) and nominal
expressions (Oact).
Let us provide an analysis of a prototypical example of a trivalent verb. In the case
of the English verb
to open
, we will have a rst actant that fulls the role of the opener
(e.g. a concierge), a second actant indicating the opened object (e.g. a door), and a
possible third actant for the instrument (e.g. a key). Note that the semantic role of the
beneciary (e.g. the client, in the phrase
the concierge opens the door with the key for
the lady
) is an extra-valent actant, as it cannot be advanced (e.g. the phrase
the key
opens the door
is incomplete but still depicts the same scene, while
the lady opens the
door changes the picture substantially).
The formal representation of the grammar characters of the morphosyntactic
material by Tesnière in its original French version [
24
] was indicated using four letters
5
The number of dependents of each governor gives the structure of the adtree, which is dened by
the Tesnerian concept of valency. Readers unfamiliar with the original concept of valency are referred to
Tesnière’s fundamental book, either in French [24] or in its English translation [25]. The relation between
Tesnerian structural syntax and CxAdGrams is claried in Gobbo and Benini [11].

the
A



q
←

O
@@
@
road
O



q
→

E
@@
@
on
U









q
→

I2
2
@@
@
a
A



q
←

O2
@@
@
long
A



q
→

O2
@@
@
rubber
O



q
←

A
@@
@
of
U



q
→

O2
@@
@
trace
O2



q
→

I2
2
@@
@@@
@@@
@@@
@
he
O1



q
←

I2
1
@@
@
left
I2







r
→
because
I2
2
@@@
@
fast
E



q
←

I2
1
@@
@
4
the suspect
O1



q
←

I2
1
@@
@
4
was driving
I2
Figure 10: The fully expanded syntactic adtree of example 1
(A, E, I, O). This notation method is preserved in CxAdGrams so as to remain consistent
with the original model. However, for technical reasons, an additional grammar
character was inserted (U) that did not exist in Tesnière’s structural syntax [24].
Direct objects of transitive verbs are often the second actant in English, and so
they will be indicated as: O
2
. In the previous example,
door
is O
2
,
concierge
is O
1
, and
key
is O
3
. True adverbs, such as
here
,
now
, or sentence adverbs—which modies the
whole phrase structure—such as obviously or technically will be indicated as: E.
Figures 10 and 11 show the fully expanded syntactic adtree of example 1 without
argumentative information. In general, this level of detail is not needed to the analyst
of arguments. Here, they were included to show how the presentation of a full sentence
appears, especially in the tabular formula of Figure 11, that would be quite similar
to an entry of a knowledge base. The reader is invited to note the presence of every
grammar character in Table 5.
As we mentioned above, although the main application of the constructive adpo-
sitional approach is (morpho)syntactic analysis, it can be applied to pragmatic and
argumentative analysis as well. This means that an element of the PTA encapsulates
an
argumentative valency
(arg-val) embedded in its own type. For instance, an argu-
ment from authority (Au) cannot be conceived without an explicit, specic actant,
fullling the role of the authority. The corollary is that the argumentative valency
is independent from the linguistic valency, although the underlining representation
mechanism is exactly the same.

because→
I2
2
→
I2
2
→E
←O
theA
roadO
onU
→
I2
2
←O2
aA
→O2
longA
→O2
←A
rubberO
ofU
traceO2
←
I2
1
heO1
leftI2
←
I2
1
fastE
←
I2
1
4(the suspect)O1
4(was driving)I2
Figure 11: The fully expanded tabular adtree of example 1
5 The design of Adpositional Argumentation
In this section we combine CxAdGrams and PTA together so to design AdArg. In order
to do so, we develop the notion of ‘argumentative adtree’ (arg-adtree). We will explain
how such an adtree makes use of all the expressive of linguistic adtrees taken from
the framework of CxAdGrams, while at the same time incorporates the pragmatic
information resulting from the argument analysis taken from the framework of the
PTA.6
In arg-adtrees, a particular emphasis is put on the rst actant, which is the sub-
ject because its identication permits to classify the argument itself as a subject or
predicate argument, as seen in Section 3. Therefore, in arg-adtrees, we consider the
argumentative valency (arg-val): as we are constructing for the purposes of the argu-
ment analysis, we put the rst actant O
1
in evidence as the leftmost subtree of the
6
Such a transformation is formally justied by the so-called conjugate construction in the formal model
of CxAdGrams—see Denition B.1.4, p. 211 in Gobbo and Benini [10].

4
σ
stm



q
←
Q
C
@@
@
4
π
stm
4
π
stm



q
→
Q
C
@@
@
4
σ
stm
Q←C
4(σ)stm
4(π)stm
Q→C
4(π)stm
4(σ)stm
Figure 12: The standard and tabular abstract arg-adtrees
given phrase. After individuating the subject, the analyst considers the argumentative
in-valent actants, that is the actants that are embedded in the type of argument in the
appropriate quadrant of the PTA. This procedure of explicitation of the in-valent actant
structure permits to clarify the inner functioning of the conclusion of the argument,
and eventually it deepens the analysis of the argument itself in terms of robustness.
Figure 12 shows the abstract arg-adtrees, in their progressive forms (on the left;
indicated by the information prominence arrow:
←
) as well as in the retrogressive one
(on the right; symbol:
→
), both as trees and as tabulars.
7
The letter
Q
as the adposition
is a placemark for a generic PTA quadrant, while the letter
C
as the grammar character
of the adposition is a placemark of the combination of the types of statements—see
Table 2.
For the sake of simplicity, we consider only retrogressive arguments, as in the
concrete examples 1–4 we are going to analyse in the following sections.
Figure 13 shows the abstract arg-adtrees of rst- and second-order retrogressive
arguments, and they correspond to the information already seen in Tables 1 and 4. In
order to illustrate how the representation works, we turn now to reconstruct examples
7
The L
A
T
E
Xpackage
adtrees
is part of the standard CTAN repository: M. Benini and F. Gobbo, adtrees—
Macros for drawing adpositional trees.
4
π
a/is/Y



q
→
α
C
@@
@
4
σ
a/is/X
4
π
b/is/X



q
→
β
C
@@
@
4
σ
a/is/X
4
π
r/is/true



q
→
γ
C
@@
@
4
σ
q/is/true
4
π
q/is/true



q
→
δ
C
@@
@
4
σ
q/is/Z
Figure 13: The abstract arg-adtrees of arguments in the four quadrants

a
sub



q
↔
π
@@
@
X
pre






q
→
α
C
@@
@@@
@
a
sub



q
↔
σ
@@
@
Y
pre
α→C(π↔(asub, X pre), σ↔(asub, Y pre ))
Figure 14: Abstract argumentative tree of alpha-arguments
1–4 in terms of the framework explained above. The examples cover all the quadrants
of the PTA, and therefore they instantiate dierent combinations of types of statements.
A caveat is needed here: in designing the Gold Standard Corpus (GSC), the decision
of including linguistic adtrees too or not is a matter of balancing time and eort, which
depends on practical considerations that are out of the scope of the present paper.
The purpose of the next sections is to clarify how to transform a syntactic adtree
into an argumentative one, in order to guarantee the possibility of having a choice
between starting from linguistic adtrees, and representing argumentative ones as tree
transformations, or encoding argumentative adtrees directly.
5.1 First-order argumentative adtrees
Figure 14 shows the abstract arg-adtree for the Alpha Quadrant. The grammar charac-
ters (
gc
) shows that that the subject (
sub
) is the same (
a
), therefore it is the fulcrum—see
section 2.1. For reasons of space, we omit the analogous abstract arg-adtrees of the
other quadrants.
In particular, the adtree of the premise (
π
) of the argument,
he left a long trace of
rubber on the road
is depicted as the leftmost subtree, while the linguistic adtree of the
conclusion (
σ
),
the suspect was driving fast
is the rightmost subtree, as the conjunction
is retrogressive, in this case
because
. For the sake of simplicity, let us concentrate on
the statement that constitutes the premise (π) of example 1 only.
A human readable representation of the syntactic adtree of this statement 1 is the
compact adtree in Figure 15, where linguistic details have been conveniently compacted
through triangles: 4.8
The in-valent arguments O
1
and O
2
are close to the main governor I
2
and they
saturate its linguistic valence one branch after the other (I
2
1
,I
2
2
). The circumstantial (E)
on the road
is peripherical, in fact it is the most distant branch from the main governor.
Figure 16 shows the correspondent argumentative adtree, and it should be put
in contrast with the syntactic adtree of Figure 15. The arg-adtree of the argument
can be derived from its linguistic counterpart by adding information that is relevant
8
In adtrees, some branches are longer than others just for human readability. Their symbolic representa-
tion does not consider these typographical details. See the bottom of Figure 14.

4
on the road
E



q
→

I2
2
@@
@
4
a long trace...
O2



q
→

I2
2
@@
@
he
O1



q
↔

I2
1
@@
@
left
I2
Figure 15: The compact syntactic adtree of example 1
for identifying the type of argument and possibly condensing information that is too
detailed for the purposes of the analysis.
First, the upmost hook does not indicate linguistic information only (

) but it marks
the whole adtree as the premise (π) and as a statement of fact (F).
Second, the subject put in evidence is not only an actant of the verb (O
1
) but a
crucial part of the argument itself (
a
, which subsumes the linguistic information). For
this reason, it is found as the leftmost sub-branch. All the rest is part of the predicate,
identied by the hook
Y
. In particular, it is worth noting that the information of the
circumstantial (E)
on the road
, while it is peripherical from a linguistic point of view,
it is central in argumentative terms, being a possible point of attack: for example, if
the trace were left not ‘on the road’ but ‘on a
rough
road’, the whole argument could
possibly collapse by doubting the statement of fact (F).
Figure 17 shows the complete compact arg-adtree of example 1. The Adpositional
Argumentation (AdArg) endevour helps the analyst both by providing an argumen-
tative valency carved into the element of the PTA, and through the analysis of the
in-valent structure. Let see an example of analysis of the latter. In example 1, the
analyst has seen that the verb ruling the conclusion (
σ
), ‘to drive’, has two actants: the
driver (O
1
) and the vehicle (O
2
). In the example, the information carried by the second
actant is unexpressed; however, that does not imply that it does not exist, rather that it
is hidden. In other words, adtrees permit to show this information under the form of a
he
a



q
→
π
F
@@
@
4
on the road
E



q
→

Y
@@
@
4
a long trace...
O2



q
↔

I2
@@
@
left
I2
Figure 16: The compact argumentative adtree of example 1

he
a



q
→
π
F
@@
@
4
on the road
E



q
→

Y
@@
@
4
a long trace...
O2



q
↔

I2
@@
@
left
I2






q
→
α
FF
@@
@
4
the suspect
a



q
→
σ
F
@@
@
4
(((
(
a vehicle
O2



q
↔

X
@@
@
fast
E



q
→

I2
@@
@
4
was driving
I2
Figure 17: The argumentative adtree of Example 1
barred subtree. Let us suppose that we have to analyse not a single argument but a
whole argumentative text. In such a case, unexpressed actants can be helpful to show
what is present in the argument structure and what is—on purpose or not—omitted.
In particular, what is interesting here is that the categorial grammar subject ‘the
suspect’, is metonymically identical with the driver O
1
, even if, strictly speaking, it is
the motor vehicle O
2
that left the long trace on the road. Interestingly, the eect in the
argument is expressed by apparently peripherical elements in the linguistic structure
of the propositions, in particular:
fast
, which is the circumstantial (E) of the conclusion
(
σ
); the second actant O
2
,
a long trace
; nally, its circumstantial (E),
on the road
. In
other words, even if circumstantials (E) represent inessential information from the
point of view of linguistic soundness, they are central for the sake of the argument: if
the suspect weren’t driving fast long traces on the road possibly couldn’t be left; in
other words, the argumentative correlation is sustained by both circumstantials (E)
and the explicit second actant O2,a long trace.
If we forget to represent the second actant O
2
(
a vehicle
) of the conclusion
σ
, we
lose an important piece of information, and that’s why it is important to represent it
in the argumentative adtree.
Let us turn our attention to example 2. As in the previous example, we rst present
the linguistic analysis of the statements in the premise and the conclusion without
including any information about the type of argument and then explain how the
transformation from the linguistic adtree (Figure 18) to the arg-adtree (Figure 19) take
place.
The linguistic adtree is rather symmetric, as the premise and the conclusion share
the same structure. The prepositional groups
on the grass
modify respectively the
subjects
Cycling
and
walking
(
O1
), and therefore it is an adjunct (grammar character:
A; see Figure 18).
Figure 19 shows the complete argumentative adtree of the example. On the top
hook, there is information regarding the quadrant (in this case,
α
) and the combination
of types of statement (indicated with a generic
C
in Figure 4) under the hook that

the
A



q
→
on
A
@@
@
grass
O



q
←

O1
@@
@
4
walking
O1



q
←

I1
1
@@
@
4
is prohibited
I1



q
→
because
I1
1
@@
@@@
@
the
A



q
→
on
A
@@
@
grass
O



q
←

O1
@@
@
4
Cycling
O1



q
←

I1
1
@@
@
4
is prohibited
I1
Figure 18: The linguistic adtree of Example 2
connects premise and conclusion. In this case, it is a combination of two factual
statements (F F ), which correspond to ‘Ef’ in the PTA (see Figure 3).
In this case, the arg-adtree appears very similar to the syntactic adtree. The subtrees
of the subjects
a
and
b
, respectively of the conclusion (
σ
) and the premise (
π
), put in
evidence the similar parts (
on the grass
), which are essential parts of the argument.
In fact, if we cut them, the resulting phrase becomes:
Cycling is prohibited because
walking is prohibited, which loses all its pragmatic force.
We argue that these two examples show that arg-adtrees are powerful tools in
order to show where the pragmatic force is placed within the linguistic material.
5.2 Second-order argumentative adtrees
Figure 13 already depicted the abstract argumentative adtrees at the second-order.
Figure 20 shows the compact arg-adtree of example 3 of the Gamma Quadrant,
War is
bad because peace is good.
Like in the case of example 2, this adtree is rather symmetric. Both the conclusion
(
σ
) and the premise (
π
) are statements of values (
V
) epistemically supported by the
speaker’s belief, represented by the umbrella term ‘true’ (
>
). As it happens in all
elements of the PTA in the Gamma Quadrant, their epistemic information is the
fulcrum—as explained in Section 3.3.
In Figure 21, nally, we pictured the arg-adtree of the example
We only use 10%
of our brain, because Einstein said so
, which can be characterized as a second-order
predicate argument combining a value with a fact (
2 pre VF
). While the statement
types are indicated under the hooks of the adtrees representing the conclusion and the
premise respectively, the information under the hook that joins them into an argument
contains pragmatic information about the argument type 2 pre being abbreviated as
δ
since that is the corresponding quadrant, and C is instantiated to VF since that is
the combination of types of statements. Dierently from the second-order arguments
in the Gamma Quadrant, those in the Delta Quadrant have one statement expressed
(or normalised) as an assertion, namely the conclusion. From comparing the arg-

adtree with the original text, the analyst will nd the fulcrum in terms of epistemic
information (symbol:
>
) as the main predicate of the conclusion. In this way, the
analysis reveals that the argument is based on a relation between the fact that Einstein
said something and the truth of that something.
As we remarked earlier, the advantage of working with adtrees is that while there
is no loss of information, the analyst may show or hide information according to
her needs and depending on the aim of the analysis. In the case of arguments from
authority such as the one in the last example, for their evaluation it is important to
know which authority is referred to. This has been made clear in the adtree by putting
‘Einstein’ into evidence.
6 Conclusion
In this paper we presented the theoretical framework of Adpositional Argumentation
(AdArg). We have shown how the existing frameworks of Constructive Adpositional
Grammars (CxAdGrams) and the Periodic Table of Arguments (PTA) can be combined
to develop a high precision tool for reconstructing and representing arguments ex-
pressed in natural language. In particular, the guidelines presented in this paper are the
necessary steps in developing a complete procedure for implementing a Gold Standard
Corpus (GSC)—for a denition and known issues, see Wissler
et al
[
33
]. In fact, whereas
the state-of-the-art in Computational Argumentation has automatized the extraction
of complete propositions and their relations, our method prepares the ground for a
more ne-grained computer-assisted analysis and evaluation of argumentative texts.
The central notion in this endeavour is that of the so-called ‘argumentative ad-
positional tree’ (arg-adtree). Apart from representing the linguistic features of the
statements that function as the conclusion and the premise of the argument under
scrutiny, such an arg-adtree contains pragmatic information regarding the order of
presentation of the statements, the type of argument they substantiate, and the argu-
mentative function of their constituents.
By providing a fully-edged reconstruction of four concrete examples of argument
types, we showed for each of the four basic argument forms in the PTA how to
transform the linguistic adtrees of the statements that are involved in the argument
into argumentative adtrees. Such a transformation permits to represent the linguistic
and pragmatic information that is relevant for the evaluation of the argument under
scrutiny.
By indicating how to apply CxAdGrams to the reconstruction of various argu-
ment types, we have further extended its analytical potential to pragmatic aspects
of discourse. In doing so, we have shown that CxAdGrams is not only suitable for
the purpose of analysing and representing aspects of language itself, but also of the
way in which language is used in communication (i.c., the persuasive eorts that are
characteristic of argumentative discourse).
While the analytical tools developed in argumentation theory mostly produce
selective representations of premises and conclusions, our reconstruction procedure
reveals linguistic and pragmatic information in greater detail. It therefore helps in
providing a more ne-grained analysis of the linguistic aspects of statements that are

Table 6: Dierent levels of aggregation of Adpositional Argumentation
level unit
micro single argument (scheme)
meso complex argumentation structures and patterns
macro argumentative genres and corpora
used in arguments. The latter is important for the subsequent evaluation of the quality
of the argumentation, because the ‘point of attack’ of a particular argument may be
found in a single word instead of in a complete proposition.
Current research in argumentation theory usually separates the analysis of the
external organisation of an argument—the so-called ‘argumentation structure’—from
its internal organisation—the so-called ‘argument scheme’. By developing the notion
of argumentative adtree, we have provided an instrument that enables an integrated
analysis of these two aspects of argumentative discourse. The whole endevour is
represented in Table 6. In particular, the argumentative discourse can be analyzed on
dierent levels of aggregation: the micro-level of a single argument (argument scheme),
the meso-level of a complex conguration of arguments (argumentation pattern or
structure), and the macro-level of complete argumentative texts or discussions—or
even argumentative corpora—within specic domains of discourse (rhetorical genres).
In this paper, we have explained a method for representing arguments on the micro-
level. However, given the features of CxAdGrams, in particular the recursive nature
of adtrees, this method can be extended for both the meso- and the macro-levels.
More in general, CxAdGrams provide a way to represent punctuation as conjunctions
between sentences, thus they permit to represent a whole text in the terms of a single,
comprehensive adtree. The implementation of annotated corpora—starting from the
GSC—represents the macro-level. Such an annotated corpus could be a huge adtree
representing the concatenations of all arguments and relevant linguistic material, such
as expressives or declarations, supporting the arguments themselves—for an example,
see again Shakespeare’s example mentioned at the end of Section 4.
AdArg is research in progress and therefore it should pass experimental validation
when it reaches a sucient mature form. In the current stage of development, we
are annotating a whole real-world argumentative speech to test the robustness of
the approach and to get feedback on what could be the next steps. In the long run
annotated corpora will be at disposal. In order to reach such a goal, the building of
corpora should be supported by a tool that implements the formal linguistic model
in computational terms. In our view, such a tool would assist the analyst in making
decisions regarding what linguistic and pragmatic pieces of information to include
in specic reconstructions of argumentative discourse. Thanks to the combination of
the linguistic and pragmatic information included in our framework with example-
based data extracted from past analyses, the aim is to partially automatize the whole
procedure using Articial Intelligence techniques, veried through robust empirical
data.

Acknowledgements
This paper is the result of a research collaboration between the founders of CxAd-
Grams, Federico Gobbo and Marco Benini, and the initiator of the Periodic Table
of Arguments, Jean H.M. Wagemans. Gobbo and Benini are mostly responsible for
Section 4, Wagemans for Section 3, whereas all other sections are the result of a joint
collaborative eort.
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4
on the grass
A



q
←
π
b
@@
@
4
walking
O1



q
←
π
V
@@
@
4
is prohibited
X








q
→
β
VV
@@
@
4
on the grass
A



q
←
σ
a
@@
@
4
Cycling
O1



q
←
σ
V
@@
@
4
is prohibited
X
Figure 19: The argumentative adtree of Example 2
peace
b



q
→

r
@@
@
good
A2



q
→

I2
2
@@
@
is
I2



q
←
π
V
@@
@
4
is true
>






q
→
γ
VV
@@
@@@
@
war
a



q
→

q
@@
@
bad
A2



q
→

I2
2
@@
@
is
I2



q
←
σ
V
@@
@
4
is true
>
Figure 20: The compact argumentative adtree of example 3

4
we only use.. .
q



q
←
π
F
@@
@
Einstein
O1



q
←

Z
@@
@
4
is said by
I3−1



q
→
δ
VF
@@
@@@
@@@
@
we
a



q
←

q
@@
@
4
only use 10% of . . .
X



q
←
σ
V
@@
@
4
is true
>
Figure 21: The compact argumentative adtree of example 4