=Paper=
{{Paper
|id=Vol-2296/paper_04
|storemode=property
|title=A Method for Reconstructing First-order Arguments in Natural Language
|pdfUrl=https://ceur-ws.org/Vol-2296/AI3-2018_paper_4.pdf
|volume=Vol-2296
|authors=Federico Gobbo,Jean H.M. Wagemans
|dblpUrl=https://dblp.org/rec/conf/aiia/GobboW18
}}
==A Method for Reconstructing First-order Arguments in Natural Language==
https://ceur-ws.org/Vol-2296/AI3-2018_paper_4.pdf
A method for reconstructing first-order
arguments in natural language?
Federico Gobbo1,2[0000−0003−1748−4921] and Jean H. M.
Wagemans3[0000−0001−9304−5766]
1
University of Amsterdam, ACLC – Amsterdam Center for Language and
Communication, Spuistraat 134, Amsterdam 1012VT, The Netherlands
f.gobbo@uva.nl http://uva.nl/profile/f.gobbo
2
University of Turin, StudiUm – Department of Humanities, via Giulia di Barolo
3/A, 10124 Turin, Italy federico.gobbo@unito.it
https://linguistica.campusnet.unito.it/persone/federico.gobbo
3
University of Amsterdam, ACLC – Amsterdam Center for Language and
Communication, Spuistraat 134, Amsterdam 1012VT, The Netherlands
j.h.m.wagemans@uva.nl http://uva.nl/profile/j.h.m.wagemans
Abstract. This paper develops a new method for reconstructing ar-
guments in natural language by combining the linguistic representation
framework of Constructive Adpositional Grammars (CxAdGrams) with
the argument classification framework of the Periodic Table of Arguments
(PTA). The method centers around the notion of ‘argumentative adposi-
tional adtree’ (‘arg-adtree’). After an explanation of the two frameworks
involved, the method is illustrated by providing the arg-adtrees of two
concrete examples of so-called ‘first-order arguments’. It is argued that
the resulting ad-trees provide a theoretically informed and empirically
reliable reconstruction of an argumentative text or discussion. As such,
the method developed in this paper is especially suitable as a point of de-
parture for developing instruments for computer-assisted argumentation
analysis.
Keywords: argumentation · Constructive Adpositional Grammars · for-
mal linguistics · natural language processing · Periodic Table of Argu-
ments.
1 Introduction
Over the last decade, computational argumentation has emerged as an indepen-
dent field of research. One of the core challenges within this field is to develop
?
This paper is the result of joint work by the two authors. Federico Gobbo is mostly
responsible for Section 2, Jean H. M. Wagemans for Section 3, whereas all other
sections are rather the result of collaborative efforts. The authors thank Marco Benini
for his thorough reading of the manuscript, and in particular for checking the parts
concerning constructive mathematics. The present paper is an amended version of a
paper submitted to the proceedings of the ISSA 2018 Conference on Argumentation.
2 F. Gobbo, and J.H.M. Wagemans
methods for representing argumentative texts and discussions so as to enable
their analysis and evaluation. So far, scholars have developed various computa-
tional models of argument that are used, for example, in developing tools for
argument mapping, argument mining and computer-aided human decision mak-
ing. A common characteristic of these models and tools is that they operate
on the level of complete propositions and the interactions between them. This
goes, for example, for approaches inspired on Dung’s abstract argumentation
frameworks, which study sets of atomic arguments and their interrelations. But
it also applies to approaches that take Walton’s argument schemes as a point of
departure, in which an argument scheme is taken to consist of a conclusion and
a set of premises [4].
In order to enable a more detailed analysis of argumentative discourse, as well
as a fruitful application of the rich but rather informal insights regarding their
evaluation developed within the adjacent field of argumentation theory, a method
for representing arguments is needed that does not only operate on the level of
complete propositions, but also on the level of their individual linguistic elements.
Such a method should represent the linguistic and pragmatic information that
is relevant for the analysis and evaluation of arguments in an adequate way. At
the same time, it should be formal(izable) to the extent that it can be used for
the purpose of building tools that automatize these tasks.
In this paper, we provide the theoretical foundation of a high precision
method for representing arguments in natural language and illustrate its work-
ing by means of examples. For the representation of the linguistic elements of
the original text, we use the theoretical framework of Constructive Adpositional
Grammars (CxAdGrams) developed by Gobbo and Benini [7]. Regarding the
identification of different types of arguments, we follow the formal linguistic
classification of the Periodic Table of Arguments (PTA) developed by Wage-
mans [12]. The combination of these frameworks is eventually aimed at devel-
oping a fully-fledged method for reconstructing argumentative discourse. In this
paper, we focus on developing the first step of this method, which is aimed at
representing the linguistic elements of the conclusion and the premise of a sin-
gle argument in such a way that it becomes possible to identify its type. In
subsequent work, we extend this first step so as to enable the representation of
concatenations of arguments within a complete argumentative text.
The method operates on the level of the individual words and therefore en-
ables the analyst to justify decisions regarding the representation of the original
text in a very detailed way, while at the same time leaving it up to the analyst
to choose which details to show and hide, according to her needs. It is a valuable
tool because it helps the analyst to identify those linguistic elements that have
a pragmatic function in the argumentation and are therefore relevant to include
in the reconstruction. The parsing largely depends on the natural language in
use, while the pragmatic information is language-independent to a large extent.
We begin our paper with providing a general explanation of the two frame-
works involved. In Section 2, we will pay attention to CxAdGrams. After having
explained the theoretical starting points of this framework, we discuss in more
A method for reconstructing first-order arguments in natural language 3
detail how the linguistic features of statements expressed in natural language
can be depicted in a so-called ‘adpositional tree’ (‘adtree’ in short). In Section 3,
we will expound the method for identifying types of arguments employed in the
PTA. We describe three basic characteristics of the various types of arguments
and subsequently describe two concrete examples of so-called ‘first-order argu-
ments’. Then, in Section 4, we combine the two frameworks so as to develop a
method for reconstructing the statements that constitute an argument. For this
purpose, we develop the notion of ‘argumentative adpositional tree’ (‘arg-adtree’
in short) and illustrate, by means of the two examples, how the linguistic and
pragmatic features of first-order arguments can be depicted in terms of such
adtrees. Finally, in Section 5, we briefly summarize and discuss our findings, sit-
uate the results within the field of formal linguistics and argumentation theory,
and indicate the main directions for further research.
2 Constructive Adpositional Grammars
Constructive Adpositional Grammars (CxAdGrams) is the theoretical frame-
work resulting from the application of constructive mathematics to the adposi-
tional paradigm in linguistics. Before explaining the constituents of the frame-
work, we will briefly indicate the meaning of ‘constructive’ and ‘adpositional’ in
this particular context. Constructive mathematics is an approach to mathemat-
ics 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 [2]. 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 first ones being proposed by Adjukiewicz [1]
and Church [3].
Of the various constructive models for natural languages so far, CxAdGrams
specifically are based on topos-theory. It thus permits to use Grothendieck’s
topoi as the mathematical instrument to formalize natural languages, and their
regularities, both intra a single language and between two or more natural lan-
guages in comparison. The linguistic and formal rules of CxAdGrams are not
discussed here for reasons of conciseness. The interested reader can see Gobbo
and Benini [7] for a comprehensive presentation of this approach to linguistic
analysis; in particular, the formal model is described in the Appendix B, which
guarantees the possibility to add pragmatic information maintaining the formal-
ity of the model. An example of pragmatic adpositional trees applied to Searle [8]
is illustrated in Gobbo and Benini [7, ch. 6].
The adpositional paradigm in linguistics follows the idea that relations be-
tween linguistic elements can be described as hierarchical in that the one element
‘governs’ the other (which then ‘depends’ on the former). A very basic exam-
ple is children play, in which play is the governing element (in short: gov) and
children is the dependent element (in short: dep).
4 F. Gobbo, and J.H.M. Wagemans
Regarding the way of representing the linguistic elements and their relations,
within the adpositional paradigm the linguistic constructions are decomposed in
terms of so-called ‘adpositional trees’ (‘adtrees’ in short). From a linguistic point
of view, adtrees represent natural language expressions in terms of recursive
trees, whose syntax will be presented – in its main traits – immediately below.
From a formal point of view, they can be seen as formulas, which means that
they are suitable for natural language processing (for an example, see Figure 7
below).
Each adtree represents a minimal pair of linguistic elements and their re-
lation, expressed in terms of adpositions. The governing element (gov) is con-
ventionally 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. Finally, the adposition (adp), which represents the rela-
tion between the governor and the dependent, is depicted as a hook under the
bifurcation of the two branches. In Figure 1, we pictured the abstract adtree
structure, adapted from Gobbo and Benini [7, p. 15].
q
↔@
adp @
gc @
4 4
dep gov
gc gc
Fig. 1. The abstract adtree structure
The triangles on the leaves indicate the possibility of recursion, i.e. the fact
that another adtree can be appended to each adtree leaf recursively, if needed.
In this case, it indicates the possibility of performing a morphological analysis of
the noun children, which is irrelevant in this context; this possibility illustrates
the fact that the analyst can hide or show details through the use of triangles,
according to her needs. The variable gc means ‘grammar character’. Gobbo and
Benini [7, ch. 2] clarify that the left and right branches of a linguistic adtrees
follow different rules of construction: while governors (right branches) can have
more dependents, dependents (left branches) can have one and one only gov-
ernor.4 In Figure 2, the adtree represents the example children play mentioned
above – the arrows above adp and respectively in Figure 1 and 2 will be ex-
plained below.
4
The number of dependents of each governor give the structure of the adtree, which
is defined by the Tesnerian concept of valency. Readers unfamiliar with the original
concept of valency are referred to Tesnière’s fundamental book, either in French [10]
or in its English translation [9]. The relation between Tesnerian structural syntax
and CxAdGrams is clarified in Gobbo and Benini [6].
A method for reconstructing first-order arguments in natural language 5
q
← @
@
4 I2 @
1
play
children
I2
O1
Fig. 2. The adtree of the phrase children play
Each proposition is analysed in terms of phrases, which are depicted as sub-
trees; 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 Ival
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 fulfilled by its dependent subtree, expressed in terms
of a definite actant value (act), i.e. a nominal expression (e.g. noun, pronoun)
that fulfils the semantic role described by the valency value itself. Actant values
are expressed by pedices both in verbs (Ivalact ) 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 first actant that fulfils 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 beneficiary (e.g. the client, in the phrase the concierge opens
the door with the key for the client) 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 [10] was indicated using four
letters (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 [10]. In Table 1 below, we provide information regarding the
meaning of the letters – adapted from Gobbo and Benini [7, p. 41].
Table 1. Grammar characters in adtrees
Value Name Function Examples
A adjunctive modifier of O adjectives, articles
E circumstantial modifier of I adverbs, adverbial expressions
I verbant valency ruler verbs, interjections
O stative actants nouns, pronouns, name-entities
U underspecified transferer prepositions, derivational morphemes
6 F. Gobbo, and J.H.M. Wagemans
Direct objects of transitive verbs are often the second actant in English, and
so they will be indicated as: O2 . In the previous example, door is O2 , concierge
is O1 , and key is O3 . True adverbs, such as here, now, or sentence adverbs –
which modifies the whole phrase structure – such as obviously or technically will
be indicated as: E. As we mentioned above, although the main application of
the constructive adpositional approach is morphosyntactic analysis, it can be
applied to pragmatics as well.
Our current purpose is to show how CxAdGrams can be applied to the re-
lation between premise and conclusion in an argument. In order to prepare the
ground for a detailed explanation of this new application, we turn now to ex-
pounding a formal linguistic approach to argument classification.
3 The Periodic Table of Arguments
The Periodic Table of Arguments (PTA) is a classification of argument that in-
tegrates the traditional multitude of incomplete, informal and sometimes even
inconsistent descriptions of the types of argument into a systematic and compre-
hensive whole.5 The theoretical framework of the table is based on three partial
characterisations of an argument, namely as (1) a first-order or second-order ar-
gument; (2) a predicate or subject argument; and (3) a specific combination of
types of statements. The superposition of these three partial characterisations
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 types of arguments described in the PTA consist of exactly one premise
and one conclusion, both of which are expressed by means of a statement that
consists of a subject and a predicate. Closely following logical conventions, sub-
jects are indicated with letters a, b, etc., predicates with letters X, Y , etc.
(predicate > having the fixed meaning ‘true’), and complete propositions with
letters p, q, etc.
The theoretical framework of the PTA distinguishes between four different
argument forms, a notion that comprises the first two partial characteristics
mentioned above. In the visual representation of the table, these forms – first-
order predicate arguments, first-order subject arguments, second-order subject
arguments, and second-order predicate arguments – correspond to four different
quadrants, which are indicated with letters α, β, γ, and δ respectively. In Table
2, for each quadrant we list the corresponding argument form and provide a
concrete example.
The argument types situated within each of the quadrants are further dif-
ferentiated on the basis of the third partial characteristic, which indicates the
combination of the types of statements instantiated by the premise and the
conclusion of the argument. For this purpose, the PTA makes use of a tripar-
tite typology of statements that distinguishes between statements of fact (F ),
statements of value (V ), and statements of policy (P ), which means that an
5
The present explanation of the theoretical framework of the Periodic Table of Argu-
ments is based on Wagemans [12, 11].
A method for reconstructing first-order arguments in natural language 7
Table 2. Overview of argument forms
quadrant conclusion premise argument (variant) example in normal form
α a is X a is Y a is X, because a is Y The suspect (a) was driving fast
(a is Y , so a is X) (X), because he (a) left a long
trace of rubber on the road (Y )
β a is X b is X a is X, because b is X Cycling on the grass (a) is
(b is X, so a is X) forbidden (X), because walking
on the grass (b) is forbidden (X)
γ q is > r is > q is >, because r is > He must have gone to the pub
r is >, so q is > (q), because the interview was
cancelled (r)
δ q is > q is Z q is >, because q is Z We only use 10% of our brain
(q is Z, so q is >) (q), because that (q) was said
by Einstein (Z)
argument can be said to instantiate one of nine different combinations of types
of statements (P P , P V , P F , V P , V V , V F , F P , F V , F F ). The argument The
government should invest in jobs, because this will lead to economic growth, for
instance, can be characterized as a P F argument since its combines a statement
of policy (P ) in its conclusion with a statement of fact (F ) in its premise.
When taken together, the three partial characterizations of argument con-
stitute a theoretical framework that allows for 2 x 2 x 9 = 36 systematic types
of arguments. Depending on the linguistic formulation of the relation between
the premise and the conclusion, each of these systematic types hosts a number
of isotopes, which are named in accordance with the existing dialectical and
rhetorical traditions of argument classification. The argument The suspect was
driving fast, because he left a long trace of rubber on the road, for instance, is to
be identified as a first-order predicate argument (1 pre) that combines a state-
ment of fact (F ) with another statement of fact (F ). The systematic name of this
argument is therefore ‘1 pre FF’. Given that the relation between the premise
and the conclusion 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 ‘effect’
for the predicate of the conclusion, driving fast, the traditional name of this
specific isotope of ‘1 pre FF’ is ‘argument from effect’. Within every quadrant,
the systematic place of the type of argument is determined by the specific com-
bination of types of statements that it instantiates (F F , V F , P F , etc.), while
the isotopes representing the linguistic variations in the traditional names are
placed in a vertical line. In Figure 3, we picture the relevant part of the current
version of the PTA – for updates and more detailed analyses of examples, see
its official web site [11].
In the next section we shall demonstrate how the theoretical framework of
CxAdGrams can be applied to the types of argument situated in the Alpha
Quadrant and the Beta Quadrant of the PTA. More in particular, we will pro-
vide an analysis of the concrete examples of arguments situated within these
quadrants that were mentioned in Table 2.
8 F. Gobbo, and J.H.M. Wagemans
Fig. 3. Quadrants Beta (left) and Alpha (right) of the PTA – Wagemans [11]
4 Combining CxAdGrams and PTA
In this section we combine the two formalisms together. In order to do so, we
will develop the notion ‘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
in the PTA.6
In arg-adtrees, a particular emphasis is put on the first actant, which is
the subject - a, as defined in the two concrete examples above - because its
identification permits to classify the argument itself as a subject or predicate
argument. In the arg-adtree that we are constructing for the purposes of the
argument analysis, this emphasis is represented putting the first actant O1 in
evidence, as the leftmost subtree of the given phrase. After individuating the
subject, the analyst considers at first in-valent actants, that is the actants that
are either explicitly expressed by the verb ruling the proposition or implied in its
semantic role structure. The procedure of explicitation of the in-valent actant
structure permits to flesh out the inner functioning of the conclusion of the
argument, and eventually it deepens the analysis of the argument itself in terms
of robustness.
A minimal argument is made of two statements, i.e. a conclusion σ, standing
for the Greek equivalent συµπρασµα (sumperasma), and a premise π, standing
for the Greek equivalent πρoθασισ (protasis). Both are expressed by means of
propositions consisting of a subject (e.g. a, b) and a predicate (e.g. X, Y ). In
order for the premise to effectively support the acceptability of the conclusion,
there should always be a common element. This yields two basic possibilities:
(1) in so-called predicate arguments, the common element is the subject, which
means that the conclusion ‘a is X’ is supported by the premise ‘a is Y ’ and (2) in
so-called subject arguments, the common element is the predicate, which means
6
Such a transformation is formally justified by the so-called conjugate construction
in the formal model of CxAdGrams – see Gobbo and Benini [7, Definition B.1.4, p.
211].
A method for reconstructing first-order arguments in natural language 9
that the conclusion ‘a is X’ is supported by the premise ‘b is X’.7 Linguistically,
each argument can be presented in two different forms: progressive and retro-
gressive – see van Eemeren and Snoeck Henkemans [5, p. 33]. The progressive
form presents at first the premise π and then the conclusion σ. In Table 2, this is
indicated by the conjunction so, which in arg-adtrees is represented formally by
a left arrow: ←. The second form is called retrogressive, as the conclusion σ is
presented before the premise π. The conjunction because is used to indicate them
in Table 2, while in arg-adtrees its formal representation is a right arrow: →.
For the sake of simplicity, since now we consider only retrogressive arguments,
i.e. our concrete examples make use of because in natural language terms and
of right arrow (→) in formal terms. Figure 4 shows the abstract adtree of first-
order predicate arguments (on the left) and the abstract adtree of the first-order
subject arguments (on the right).
q q
→@ →@
α @ β @
4 C @ 4 4 C @ 4
π σ π σ
a/is/Y a/is/X b/is/X a/is/X
Fig. 4. The abstract argumentative adtrees of first-order arguments
The Greek letters alpha and beta (α, β) in the hook indicate the respective
quadrants in the PTA. In the concrete examples below, the subtrees indicating
the linguistic material will be always identified with an epsilon (), put in the
hook, or by linguistic material directly, for reasons of compactness. Finally, the
letter C indicates the combination of types of statements, which in concrete
examples can take the values of F F , V F , P F , etc.
In order to illustrate how all this works, we turn now to reconstructing two
examples in terms of the framework explained above. The examples are both
first-order arguments, one being a predicate argument and the other a subject
argument, and they instantiate different combinations of types of statements.
Example 1: An argument from effect The first example we analyse is The
suspect was driving fast, because he left a long trace of rubber on the road. It has
been identified as a first-order predicate argument that supports a statement
of fact with another statement of fact, and its trivial name is ‘argument from
effect’. In the PTA, this type of arguments is indicated by means of the symbol
‘Ef’ (see Figure 3). In order to analyse this example in terms of CxAdGrams,
7
What follows is a different presentation of the illustration of Figure 1 in Wage-
mans [12, p. 4]. Here, the roles of the subjects and predicates are put in more
evidence.
10 F. Gobbo, and J.H.M. Wagemans
q
→@
because
I22 @←q
@
@
@
q I1 @←q
2
→ @ fast @
@ @
I22 @→q
E
4 I21 @4
@
@ the suspect was driving
q I 2 @
← @ 2 @ O1 I2
@
q O2 @q
@@
→@ a →
@ @
@ @
q E @
A
O2 @q
@
@
←@ on long →
@ @
@ @
O @
U A q O2 @ @q
@
the road ←@ trace ←@
@ @
A O O2
A @ I21 @
rubber of he left
O U O1 I2
Fig. 5. The fully expanded linguistic adtree of Example 1
we first present the linguistic analysis of the statements in the premise and the
conclusion without including any information about the type of argument. We
will then explain how the transformation from the linguistic adtree to the arg-
adtree takes place.
Figure 5 illustrates the linguistic adtree of the example.8 In particular, the
linguistic adtree of the premise (π) of the argument, he left a long trace of rubber
on the road is depicted as the mostleft 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. The reader is invited to note
the presence of every grammar character mentioned in Table 1.
The arg-adtree of the argument can be derived from its linguistic counterpart
by adding information that is relevant for identifying the type of argument and
by condensing information that is too detailed for the purposes of the analysis.
For the sake of simplicity, let us concentrate at the premise (π) first. Figure 6
shows the transformation from the linguistic to the arg-adtree. Linguistic details
– already illustrated in Figure 5 – have been conveniently compacted through
triangles: 4.
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 ). Then,
8
In adtrees, some branches are longer than others just for human readability. While
linearised for machine coding, all branches become equally long.
A method for reconstructing first-order arguments in natural language 11
q
q →@
→ π @
F @q
@
@
I 2 @q he →
4 2 →
@
@
a
Y @q
@
on the road @
I2 @↔q
2 4 ↔
E 4 @ on the road
@
@
a long trace... @ I2 @
E 4 left
O2 I21 @
he left a long trace...
I2
O1 I2 O2
Fig. 6. The transformation from linguistic to argumentative adtree
the subject put in evidence is not only an actant of the verb (O1 ) 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, identified by the hook ypsilon (Y ). The reader is invited to note the
corresponding linearised form of the argumentative adtree (Figure 7), useful for
constructing a treebank of arg-adtrees suitable for natural language processing.
π→ → ↔
F (hea , Y ((on the road)E , I2 ((a long trace...)O2 , leftI2 )) )
Fig. 7. Linearisation of the argumentative adtree (Figure 6, right)
Figure 8 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 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).
CxAdGrams help the analyst through the analysis of the in-valent structure.
In fact, the analyst has seen that the verb ruling the conclusion (σ), ‘to drive’, has
two actants: the driver (O1 ) and the vehicle (O2 ). In the example, the information
carried by the second actant is unexpressed; however, that does not imply that
it does not exist, rather that is hidden. In other words, adtrees permit to show
this information under the form of a 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 sub-
ject ‘the suspect’, is metonymically identical with the driver O1 , even if, strictly
speaking, it is the motor vehicle O2 that left the long trace on the road. Interest-
12 F. Gobbo, and J.H.M. Wagemans
q
→@
α @
FF @q
→@
σ @
q F @q
→@ 4 ↔@
π @ the suspect @
F @q a 4 X @q
he →@ →@
a @ ( a vehicle
((( @
Y @q I2 @4
4 ↔ @ O2 fast
on the road @ was driving
E
E 4 I2 @ I2
left
a long trace...
I2
O2
Fig. 8. The argumentative adtree of Example 1
ingly, the effect 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 premise (π); the second actant O2 , a long trace; finally,
its circumstantial (E), on the road. In other words, even if circumstantials (E)
represent inessential information from the point of view of linguistic soundness,
on the contrary 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 O2 of the conclusion σ, we risk
to lose an important piece of information, and that’s why it is important to
represent it in the argumentative adtree.
Example 2: An argument from analogy The second example we analyse
is Cycling on the grass is forbidden, because walking on the grass is forbidden.
In Section 3, this example has been identified as a first-order subject argument
linking a statement of value to another statement of value. The systematic name
of the argument type is ‘1 sub VV’ and its trivial name is ‘argument from
analogy’. In the Periodic Table of Arguments, it is indicated by means of the
symbol ‘An’ (see Figure 3). Like with the previous example, we first 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 9) to the arg-adtree (Figure
10) takes place.
The linguistic adtree is rather symmetric, as the premise (π) and the conclu-
sion (σ) share the same structure. The prepositional groups on the grass modify
A method for reconstructing first-order arguments in natural language 13
q
→ @
because
q
@
←
I11 @
@ @
@
q I1 @ @q
@
← @ 1 4 ←
@
@ is prohibited @
q O1 @ q I 1 @
→@ 4 I1
←@ 1 4
on @ walking @ is prohibited
A @ q O1 @4
the grass O1 → @ I1
on @ Cycling
A O
A @
the grass O1
A O
Fig. 9. The linguistic adtree of Example 2
respectively the subjects Cycling and walking (O1 ), and therefore it is an adjunct
(grammar character: A; see Figure 9).
q
→@
β @
VV @q
←
@
σ @
q V @4
←@
σ @ is prohibited
q a @
← @ 4 4 X
π @ on the grass Cycling
q V @4
← @ A O1
π @ is prohibited
4 b @4 X
on the grass walking
A O1
Fig. 10. The argumentative adtree of Example 2
In this case, the arg-adtree (Figure 10) appears very similar to the linguistic
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.
14 F. Gobbo, and J.H.M. Wagemans
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 Conclusion
In this paper we demonstrated how the theoretical frameworks of Constructive
Adpositional Grammars (CxAdGrams) and the Periodic Table of Arguments
(PTA) can be combined so as to develop a high precision tool for the reconstruc-
tion of arguments in natural language. The central notion in this endeavour is
that of the so-called ‘argumentative adpositional tree’. 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 type of argument.
By providing a fully-fledged reconstruction of two examples of so-called ’first-
order arguments’, we showed how to transform the linguistic adtrees of the state-
ments involved into argumentative adtrees. Such a transformation permits to
represent the argumentative text or discussion including all information that
may turn out to be relevant for its evaluation. Whereas the state-of-the-art
in computational argumentation has automatized the extraction of complete
propositions and their relations [4], our method prepares the ground for a more
fine-grained computer-assisted analysis of argumentative texts.
By indicating how to apply CxAdGrams to the reconstruction of argument
types, we extend 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 lan-
guage is used in communication (i.e., the persuasive efforts that are characteristic
of argumentative discourse). Present research in argumentation theory usually
separates the analysis of the external organisation of the argumentation – the so-
called ‘argumentation structure’ – from the internal organisation of an argument
– 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. Also, while the analytical tools
developed in argumentation theory mostly produce selective representations of
premises and conclusions, our reconstruction procedure reveals pragmatic infor-
mation in detail. It therefore helps in providing a more fine-grained analysis of
the linguistic aspects of statements that are used in arguments.
As we indicated in the introduction, the research presented in this paper
is the first step in developing a complete procedure for reconstructing argu-
mentative discourse. In this endeavor, the method for creating argumentative
adtrees can be extended to second-order arguments. Another extension would
be to apply the procedure to concatenations of arguments, thereby providing a
complete analysis of an argumentative text. In fact, 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.
A method for reconstructing first-order arguments in natural language 15
Finally, the formal linguistic model presented here could be implemented in
a computational model under a form of a tool. Such a tool would assist the
analyst in making decisions regarding what linguistic and pragmatic informa-
tion to include in specific 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 Artificial Intelligence techniques.
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