Adpositional Argumentation (AdArg) is a new method for annotating argumentative discourse that represents linguistic and pragmatic information in argumentative adpositional trees. In this paper, we explain how the representation of claims and individual arguments provide the building blocks for more complex argumentation structures. We illustrate the abstract trees representing the systematic possibilities of a claim (one statement), minimal argument (one conclusion, one premise), convergent argumentation (one conclusion, multiple premises), as well as serial argumentation, when the same linguistic material plays the double role of the premise of a given argument and the conclusion of a subargument. computational argumentation, argumentation theory, argumentation structure, complex argumentation Developing tools and models for annotating natural argumentative discourse requires a formalization of linguistic material. A major challenge in this endeavor is to find the right balance between, on the one hand, the level of linguistic detail to be incorporated in the tool or model and, on the other hand, its robustness from a formal point of view. In many approaches, the concessions are made on the linguistic side. The tools based on Walton's argumentation schemes [1] and the Toulmin model [2], for instance, produce selective representations of premises and conclusions but they do not consider a great many linguistic items relevant for identifying the fabric of the argumentation. Computational models suitable for argument mining, for instance those based on Dung's seminal paper on abstract argumentation [3], usually abstract away from linguistic details in representation the argumentation [4, 5].
LGOBE Artificial Intelligence (AI 32021), 01 − 03, 2021, ,
https://federicogobbo.name/ (F. Gobbo); https://marcobenini.me/ (M. Benini);
https://uva.academia.edu/JeanHMWagemans (J. H.M. Wagemans)
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material completely intact, enabling the analyst to hide or highlight aspects relevant for their
purposes. In earlier work on AdArg, it is explained how the linguistic representation framework
of Constructive Adpositional Grammars (CxAdGrams) [
The general goal of AdArg is to explicate the process of annotating natural argumentative discourse through a detailed representation of linguistic as well as pragmatic information. We argue that the formal representation of the dynamics and the results of such a process eventually facilitates textual analysis for humans as well as machines. So far, we have focused on describing how our method can represent individual arguments of various types, while acknowledging that actual argumentative discourse usually consists of a more complex whole of conclusions and premises.
In this paper, we stay at the highest level of abstraction possible, hiding the linguistic
details in the small triangles (△; see all Figures below). In particular, we first explain how the
representations of individual arguments provide the building blocks for complex argumentation
structures. Then, we show how our method deals with complex argumentation starting from the
notions of ‘minimal argument’ and ‘argument form’ described in the PTA, already presented in
previous publications [
In the theoretical framework of the PTA, a ‘minimal argument’ is defined as a combination of
two statements, one of which functions as the conclusion ( ) and the other as the premise ( ).
The ‘argument form’ of a minimal argument is the specific configuration of the subjects and the
predicates of these two statements, after the analyst has reconstructed their original linguistic
expression into the retrogressive normal form (conclusion, because premise) [
The unfolding of the minimal argument forms shows the fundamental structures of abstract arg-adtrees. Figure 2 illustrates that the structure of Alpha, Beta, and Gamma arguments consists of diferent configurations of subjects (
, ) and predicates ( , ) of the propositions ( , )
involved, while the premise of Delta arguments has a predicate ( ) attributed to the conclusion,
which appears in the arg-adtree as quoted ( ) [
△ a|b|b q Pta Pta △ Z △ X 2The “is true” (is ⊤) that is added to the second-order arguments of the Gamma and Delta quadrants is not a logical value but expresses in natural language the standardized doxastic commitment of the arguer to the acceptability of the proposition.
Unlike minimal arguments, complex arguments have either multiple premises or use the premise ( ) as the conclusion ( ) for a subargument, i.e., an argument depending on the main one: the ifrst ones are right-growing, called convergent, while the second ones are called serial. Serial arguments are so called because they provide a complex argument which is, literally, a chain of minimal arguments. Convergent arguments consist of one conclusion ( ) supported by the ifnite multiple premises ( 1, 2,…, ). The conclusion may be supported by diferent types of arguments, depending on the specific minimal argument form identified when analyzed in isolation.
△ 1 q txt
In serial arguments, the same linguistic element (txt) plays the role both of the premise ( 1) of the hierarchically highest argument and of the conclusion ( 2) of the subargument. To represent this double function of txt, the notation ( represents the two halves of a chain ring. Specifically, ( 1, 2) is used, in which the graphically 1, 2) represents the reason why the two arguments can be joined. The intuition is that 2 implies 2 = txt = 1, which in turn implies 1. The verb implies clearly shows that the logic of the arguer comes in here: whatever notion of implication she uses, it has to interpolate 2 and 1 through txt. For example, if the arguer uses classical logic, implies would be the Aristotle’s implication ⊃, thus ( 1, 2) stands for the logical tautology ( 2 ⊃ ) ∧ ( ⊃
1), explaining how the arguments meet on , which gets instantiated to txt. However, the arg-tree representation is pre-logical, and it does not force any specific way to interpret . In fact, whatever notion of implication ⊃ and meet3 ∧ the arguer uses, it has to support the fact that ( 2 ⊃ txt) ∧ (txt ⊃ 1). Hence, the argumentation conveys also a snapshot of the logic of the arguer, and it is contained in the representation tree. This marks a huge diference with most other approaches, in which the logic is presumed.
In this paper we have described how AdArg represents various constellations of argumentative statements expressed in natural language. The representation results in an annotation of the discourse that reveals argumentation structures and patterns. This annotation is pre-logical: it shows exactly where the logic comes in, and thus, in the eyes of the argumentation analyst, it 3The name is not by chance, reminding to the interpretation of conjunction in algebraic lattices. makes evident the point of attack of the way of reasoning, i.e., the logic of the arguer. To explain this aspect in full, an empirical analysis that comprises linguistic and pragmatic elements is needed; this is left as a further work. Moreover, the proposed representation shows how the logic of the arguer can be partially inferred from the used arguments, specifically by showing how she believes arguments can be validly connected in sequences.
We claim that a rigorous and fine-grained annotation of arguments expressed in natural language can lead to the building of corpora suitable for processing in terms of argument mining and eventually Explainable AI.