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Diagramming the Enthymematic Structure of Counterarguments. An Introduction to IAMT Diagrams

Andrea Rocci et Costanza Lucchini
Traduction(s) :
Cartographier la structure enthymématique des contre-arguments. Introduction aux schémas IAMT [fr]

Résumé

In this work, we examine the issues encountered by different approaches to argumentation diagramming in dealing with a simple pattern of concession and counterargument in monological discourse, focusing, in particular, on the complementary strengths and weaknesses of Inference Anchoring Theory (IAT), an approach oriented towards discourse annotation, and of the Argumentum Model of Topics (AMT), which focuses on the in-depth reconstruction of enthymemes and argument schemes. We then propose a new combined framework, called IAMT, for diagramming enthymemes representing at once the inferential steps realized and their relation to the discourse structure. We show how the IAMT diagram allows to fully represent the reconstructed inferential structures both of the counterargument and of its target and their logical interaction, while anchoring them to the sequential dispositio of the concession and counterargument pattern.

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Introduction

  • 1 As an acronym, the label IAMT might be read as Inference Anchoring Model of Topics. But, in fact, t (...)

1This paper introduces a new method of argument diagramming, namely the IAMT1 approach, which results from the integration of two established frameworks: Inference Anchoring Theory (IAT; Budzynska and Reed 2011, Budzynska 2013) and the Argumentum Model of Topics (AMT; Rigotti and Greco 2019). We show that the integrated IAMT approach overcomes the respective difficulties encountered by the two parent frameworks in adequately mapping the functioning of patterns of concession and counterargument, which are a pervasive and characteristic feature of argumentative discourse, and which have been found to be particularly challenging to represent diagrammatically (Rocci 2021). More generally, we argue that IAMT diagramming is particularly apt to support the in-depth study of enthymemes in discourse.

  • 2 The terms “implicated premise” and “implicated conclusion” originate from Relevance Theory (Sperber (...)

2The recourse to diagrams for elucidating the reasoning chains conveyed in argumentative discourse presupposes that this reasoning is not trivially discernible at the surface of the text, at least not in a way that is sufficient to enable systematic argument classification, argument criticism and evaluation or studies of the contextual persuasiveness of argument types. In fact, arguments, like any other meaning, are not “in the text” but are the result of a pragmatic inferential process of interpretation integrating rich contextual information (cf. Rocci 2006, Oswald 2023). Most arguments in ordinary discourse are enthymematic. An enthymeme, in its most common understanding, “is an argument that has one or more premises, or possibly a conclusion, not explicitly stated in the text, but that needs to have these propositions explicitly stated to extract the complete argument from the text” (Walton 2001: 93). While the notion of enthymeme originates in Ancient Rhetoric (cf. Bitzer 1959), its use has since crossed into linguistic pragmatics (Rocci 2006, Breitholtz 2021) to describe arguments whose understanding and acceptability requires the recovery of “implicated premises” and the derivation of “implicated conclusions”2.

3The approaches to diagramming used in argumentation greatly differ in the extent of their coverage of enthymemes. As detailed in section 1, these methodologies differ along two axes, one corresponding to the distinction between accounts of the inferential microstructure of individual arguments and the mapping of the macrostructure of complex argumentation, the other corresponding to the tension between approaches inspired by linguistic annotation, seeking to enrich textual data with information about argumentation structure while maintaining a close and traceable connection with the sequence of discourse units in the original data, and approaches aimed at the reconstruction of arguments in a canonical form, which can involve a pretty radical reconfiguration of the original data.

4The two parents of the proposed IAMT framework sit in the two opposite corners of this two-dimensional space: while IAT is a macrostructural annotation approach aimed at preserving the connection between the inferential structures of argument and the succession of units in the discourse being analyzed, AMT is an approach aimed at the reconstruction of the inferential microstructure of individual arguments. As will be shown in section 3, the two approaches encounter complementary difficulties in the analysis of patterns of concession-counterargument in discourse.

5A concessive discourse move consists of the presentation of an argument that someone has either previously presented or could conceivably use, to which the speaker partially commits without committing to the conclusion it leads. A counterargument, on the other hand, consists of the presentation of reasons against the acceptance of the conclusion of the conceded argument. The understanding of these patterns, often signaled by linguistic markers of concession and contrast, involves the evocation of (at least) two arguments, whose manifestation is typically largely implicit, requiring not only the recovery of implicit premises but also typically the derivation of implicit conclusions. The pattern also involves establishing a relation of logical conflict between the two arguments, which can impinge upon different explicit or implicit components of the arguments.

6A macrostructural annotation-oriented approach such as IAT proves inadequate for the analysis of these patterns, as it fails to account for implicit elements and lacks a sufficiently fine-grained inferential structure to map the conflict relation. Conversely, AMT diagrams only present the fully explicated inferential structures of individual arguments but have no established way to represent conflict, and, while incorporating unstated premises, do not clearly distinguish between what is explicitly stated and what is inferred, nor have a way to link the propositional contents involved in the arguments to the illocutionary intent (e.g. conceding vs rebutting) associated with the moves.

7In contrast, by combining these complementary models, IAMT elucidates the microstructure of argumentative discourse, detailing how individual inferential steps relate to sequences of discourse utterances. Specifically, IAMT enables the reconstruction of argument schemes and of the endoxical, culturally shared premises on which inferences rely while simultaneously linking these inferential configurations to discourse sequences and turn-taking structures. This dual focus on discourse annotation and inference reconstruction facilitates the study of the micro-dispositio of argumentation and of the explicit-implicit division of labor in argumentative discourse. These features make IAMT particularly suitable for small corpus studies, especially those assembling collections of instances of specific argumentative phenomena.

8The present study is structured as follows. Section 1 reviews existing methods for diagramming argumentation discussing differences along the macrostructure – microstructure and the annotation – reconstruction axes. Section 2 explores the diagramming of concession and counterargument and assesses existing diagramming approaches for these structures, including a previous attempt by one of the authors (Rocci 2021). Section 3 introduces IAT and AMT, demonstrating how IAMT obtains from their integration and applies IAMT to the analysis of examples of concession and counterargument, illustrating its functionality, advantages, and limitations.

1. Structure, annotation and reconstruction

1.1. Microstructures and macrostructures

9The investigation of argumentation structures is closely intertwined with the analysis of natural language at different levels. Freeman (2011: 1) distinguishes between microstructure, which pertains to the internal structure of individual statements, and macrostructure, which concerns the organization of argumentative relations among statements, that is, how the component statements of an argument “fit together as wholes to allegedly lend support to some claim or claims.” While both dimensions are essential for a comprehensive understanding of argumentation, most studies tend to focus on the latter, examining how argumentative units interact within a text while often overlooking the microstructures of individual arguments. Many diagrammatic approaches in argumentation theory, including those developed by Freeman (2011), primarily operate at the macrostructural level, capturing how statements interconnect to form argumentative wholes. However, analyses of argument schemes – templates of reasoning that warrant inferential connections between premises and conclusions – seem to cross the boundary of this dichotomy. On the one hand, argument schemes are concerned with multiple premises working together to justify a conclusion; on the other, they are strictly related to the formulation of individual statements, often necessitating their reformulation into a canonized version to highlight their alignment with the scheme.

10The Argumentum Model of Topics (AMT), as formulated by Rigotti and Greco (2019), is primarily a “micro-approach to the analysis of what we call the inferential configuration of single argumentations” (Rigotti and Greco 2019: 5), focusing on the inferential configuration of individual arguments; only secondarily can it be extended to complex argumentation. In contrast, Inference Anchoring Theory (IAT) is predominantly a macrostructural model of extended stretches of argumentative dialogue or text, analyzing how argumentative moves unfold within discourse.

1.2. Annotation vs reconstruction

11Beyond their focus on micro- vs. macrostructures, approaches to diagramming argumentation also differ in terms of depth, that is, the extent to which structural representations diverge from the linguistic surface of the original text. In this respect, we can observe a continuum ranging from the pole of annotation, where labeled structures and relational links are added onto the explicit discourse, to the pole of reconstruction, where a range of extensive transformations such as addition, deletion, rephrasing, and reordering is applied to the analyzed discourse in order to obtain what van Eemeren and Grootendorst (2004: 95), using a metaphor from early Chomskian linguistics, call the “argumentative ‘deep structure’ of the discourse or text.” As we will discuss more in detail the following section 3, while IAT represents an annotation-oriented approach, AMT can be seen as closer to the reconstruction pole.

12Diagramming efforts close to the annotation end of the continuum include attempts by Azar (1999) and Green (2010) to use Rhetorical Structure Theory (RST) (Mann and Thompson 1988, Mann and Taboada 2006), a diagrammatic model of discourse coherence postulating a set of relations holding between discourse utterance, as a starting point for mapping argumentation macrostructures. Peldszus and Stede (2013: 17-19) also examine the suitability of RST to serve as a basis for argumentation mapping. Among other things, they note that RST imposes strict constraints on the attachment of units to a discourse structure that formally corresponds to a tree diagram so that long-distance dependencies – such as the recovery of a premise from a non-adjacent passage – become problematic. Peldszus and Stede (2013) propose their own approach to annotating argumentation in texts. Their analysis starts with the recognition of argumentatively relevant passages (argumentative discourse units, ADUs), and then links ADUs adopting a set of support and attack relations inspired by Freeman’s (2011) work and a system for restatement, to deal with situations where either the main standpoint or an argument is repeated or reformulated in different, non-adjacent text passages. Peldszus and Stede’s framework (2013) also provides a detailed treatment of counterargument, which we will discuss briefly in Section 2.

13One issue that emerges in discussions of RST-like analysis for argument diagramming (cf. Green 2010, Peldszus and Stede 2013) is the enthymematic nature of argumentation: arguments in ordinary discourse often require the audience and analyst to supply implicated (or presupposed) premises. Peldszus and Stede (2013) take the stance of not including implicit premises in their diagramming system, deferring their suppletion to a later and deeper stage of analysis based on argumentation schemes. In the following sections, we will further discuss the problem of implicit premises as well as the problem of arguments with tacit conclusions. It is worth mentioning already, however, that, contrary to the problem of recovering the implicit premises providing a warrant for an argument, this second problem cannot be deferred to a later stage of analysis. In the absence of explicit standpoints or conclusions, approaches closer to the annotation pole risk completely missing the argumentative nature of a passage or suggesting unsatisfactory or misleading analyses with the direct linking of units whose relationship is, in fact, mediated by a tacit standpoint. This will be an important point of our discussion of counterargument diagramming in sections 2 and 3.

2. Diagramming counterarguments and their implicit conclusions

2.1. Counterarguments as enthymematic structures

14A counterargument is a discourse move that involves the presentation of reasons against the acceptance of an extant target argument. Following Rocci (2021), we use the term counterargument in a general sense. In line with a broad tradition within argumentation studies, we adopt more specific terms, such as rebutter of a conclusion, rebutter of a premise, and undercutter, to refer to the different ways in which counterarguments can interact inferentially with the target argument (cf. Pollock 1987).

15Within an argumentative discussion, counterarguments are intrinsically linked to concession. By presenting a counterargument, an arguer implicitly acknowledges that the target argument has been (or could be) put forward, thereby conceding that the opposing party has at least articulated some form of reason, which entails recognizing the argument as a prima facie reason in Pollock’s (1987) sense – something that, in the absence of a counterargument, could be (or was) accepted as a defeasible reason. The interplay between concession and counterargument is particularly evident in “Yes, … but” patterns found in both dialogical and monological discourse, explicitly signaling this argumentative dynamic.

16Relatedly, certain kinds of counterarguments provide evidence that argument evaluation requires reconstruction, specifically reconstructing the whole enthymematic underlying structure. As observed by Rocci (2021: 144), arguers often engage in a “naïve” reconstruction of the conceded target argument by countering utterances that are interpreted as supporting implicit standpoints, as illustrated in example (1) below.

(1) Father: It’s already well past nine, and tomorrow you have school.

Child: But I’m not tired, Dad!

17The child’s reply in (1) is coherent only inasmuch as the father’s utterance is understood as supporting an implicit standpoint such as “It’s time to go to bed.” Recovering this implicit standpoint is essential for establishing the coherence of the dialogue and for understanding the dynamics of the counter-argumentative move. In this sense, the diagramming of counterarguments clearly exemplifies the tension between annotation and reconstruction discussed in the previous section, making it a particularly suitable case study for demonstrating the value of IAMT. By integrating in-depth reconstruction of enthymemes with the systematic anchoring of these structures within sequences of speech acts in discourse, IAMT offers a comprehensive approach to diagramming counterarguments.

2.2. Representing Counterarguments and Concessions

18In this section, we examine two existing methods for diagramming counterarguments, as proposed by Peldszus and Stede (2013) and Rocci (2021), applying them to an example to demonstrate their limitations and motivate the need for an integrated model. Particular emphasis is placed on Rocci’s (2021) approach, which serves as the foundation for our proposed method.

  • 3 Although OVA was designed from the outset to apply the IAT framework (detailed in section 3), it ca (...)

19The diagrams used to analyze the example utterances are drawn using the Online Visualization of Argument (OVA) platform (Janier et al. 2014); now in its third major iteration, OVA (Janier et al. 2014) is an interface for the analysis of arguments online, implementing the formal structure of the Argument Interchange Format (AIF, Chesñevar et al. 2006)3.

20The example consists of two short passages from an opinion article published in The New York Times in February 2021 on the topic of distance teaching via videoconferencing platforms. The author, Viet Thanh Nguyen, expresses a favorable view of this teaching modality, which, at the time of writing, was a necessity for educators worldwide. From the outset, he frames his stance as a contrarian, stating: “Here’s an unpopular opinion: I like teaching on Zoom.” In line with this contrarian positioning, the article repeatedly employs micro-patterns of concession and counterargument, elliptically evoking the perspective of an implicit, unnamed opponent, which we can identify with the “majority view.” We analyze two micro-examples: (2) comprises the headline and supporting headline (strapline) of the article, while (3) is drawn from its body.

(2) I Actually Like Teaching on Zoom. There may be less human warmth. But there can be more human connection.

(3) If a lecture is only someone talking for an hour, that can indeed be stultifying on video – but that would also be true in a classroom.

Both examples present different explicit linguistic markings of adversativity (“actually,” “but”) and concession (“may,” “if”).

21In their annotation system for argumentative discourse, Peldszus and Stede (2013) propose a systematic approach to annotating counterarguments, reviewed in detail in Rocci (2021), drawing from Freeman’s (2011) argument macrostructure analysis. Peldszus and Stede (2013) propose that including counterarguments in argumentation diagrams requires introducing, alongside support, a different type of edge called “attack” (cf. Dung 1995). Given a minimal argument diagram consisting of a premise and conclusion connected by a support relation, attacks may target the acceptability of either the premise or the conclusion, giving rise to the rebutter of the conclusion and the rebutter of the premise. Alternatively, the attack may concern the relevance of the premise to the conclusion, giving rise to an undercutter, and in this case, the target of the attack in the diagram is the support edge itself.

Fig. 1: Representing counterarguments according to Peldszus and Stede (2013)

22The diagram in Fig. 2 represents the analysis of (2) according to Peldszus and Stede’s (2013) diagramming style; the conceded argument “There may be less human warmth” is represented as a rebutter of the conclusion, while “But there might be more human connection” offers support to it.

Fig. 2: Analysis of (2) according to Peldszus and Stede (2013)

Is the diagram in Fig. 2 a satisfactory analysis of the concession and counterargument pattern in example (2)? In fact, there are two reasons for considering it unsatisfactory.

23(i) First of all, we need to observe that what is mapped as a counterargument, specifically as a rebutter of the standpoint, is the conceded argument that the author attributes to the “majority view.” Such an analysis makes sense if we adopt what we might call a perspectival notion of counterargument, i.e. we call counterarguments the arguments of the opponent in that they go against the argument supporting the author’s standpoint. Sometimes people actually do use the word counterargument to mean something like that. If we do so, however, the expression “concession and counterargument pattern” does not make much sense because here, the conceded argument is the counterargument. When we introduced this pattern, we adopted instead a sequential notion of counterargument as a contrast to the acceptance of an extant target argument, i.e., an argument that is already part of the discourse context or common ground. According to this view, the target would be the “majority view” (the conceded argument), while the counterargument would be the author’s contrarian viewpoint that seeks to rebut it. The choice is one of definition but is not merely terminological. There are reasons to believe that the sequential notion is much more helpful. It is not possible here to discuss them thoroughly; we will be content, then, to briefly mention the most prominent ones. First of all, while the perspectival notion is restricted to monologue, the sequential one can apply uniformly to the analysis of dialogue (where it’s not possible to adopt one perspective!) and to monological discourse where the dialogistic strategy of concession is at work. Secondly, in view of argument evaluation, the sequential notion is consistent with the dynamics of defeasible reasoning, as outlined by Pollock (1987) and allows to adopt his rich notion of rebutter: a (successful) rebutter not only provides reasons for not accepting the target conclusion but provides explicitly reasons for not accepting it notwithstanding the “prima facie reason,” i.e. the extant argument supporting it (cf. Pollock 1987: 485 and the discussion in Rocci 2021).

24(ii) Even if we were to prefer the perspectival account, however, the style of diagramming exemplified in Fig. 2 would still be problematic. As we move to example (3), we can observe that it is impossible to use the same style of diagramming to consistently represent the conceded argument of the “majority view” (i.e. “if a lecture is only someone talking for an hour, that can indeed be stultifying on video”) as an attack on some aspect of the author’s argument. Firstly, for the trivial reason that in (3) the author’s argument does not have an explicit conclusion, and the attack relation would have nowhere to target. Secondly, for the less trivial reason that in (3), the author does not have a substantial standpoint (either explicit or implicit) but is simply undercutting the majority view’s argument. In conclusion, the style of diagramming exemplified in Figure 2 does not even consistently capture a perspectival notion of counterargument.

2.2.1. A systematic model for counter-argumentative structures

25The first step to overcome the problems encountered in the previous section is to move towards reconstruction and admit that we need to enrich our structure with implicit conclusions/standpoints. The proposal in Rocci (2021) provides a first attempt to solve the issue moving in this direction. This approach is based on two key insights. The first, drawn from Pragma-Dialectics (cf. van Eemeren et al. 2007: 193), is that any counterargument, from a dialectical perspective, entails a difference of opinion between two opposing standpoints. The second insight concerns the recognition that, inferentially, counterarguments are arguments in their own right: “their ability to function as [...] attacks against a target argument depends on their more fundamental nature as arguments capable of supporting the inference of a conclusion” (Rocci 2021: 151). A counterargument does not merely negate or challenge another argument, but it does so by constructing and justifying an alternative standpoint.

26As a consequence, the relation of attack is abandoned or rather decomposed into a relation of confrontation and a relation of argumentative support: a counterargument thus consists in the presentation of a premise supporting a, possibly implicit, conclusion which is in a relation of confrontation and, hence, purported incompatibility with a part of the target argument. As shown in Rocci (2021: 156), the three fundamental types of counterarguments (rebutter of the conclusion, rebutter of the premise, and undercutter) can be easily translated into these terms.

27Fig. 3 and 4 represent the diagrams of (2) and (3) according to Rocci (2021). We use a color-coded version of the OVA diagram to express additional information about the reconstructive operations carried out. Note that, in these figures, OVA’s red conflict node has been reinterpreted as indicating confrontation rather than attack.

Fig. 3: Analysis of (2) in the style of Rocci (2021)

Fig. 4: Analysis of (3) in the style of Rocci (2021)

28The diagrams in Figs. 3 and 4 reconstruct the full inferential chains supporting the standpoints and assume a sequential conception. In both instances, the conceded argument constitutes the target, while the author’s argument is the intervening counterargument. Furthermore, considering Viet Thanh Nguyen’s contribution as a counterargument does not obscure the fact that it is in itself an argument. In fact, both target and counterargument are represented as fully fledged arguments.

29In the color-coded diagram, the reconstructed implicit standpoints are represented in grey. In the case of (2), we see that the target’s standpoint [1.] is implicit, while the author’s standpoint [2.] is explicit. The configuration mapped for (2) in Fig. 3 amounts to a rebutter of the conclusion, and the confrontation between [1.] and [2.] corresponds to the main confrontation underlying the entire opinion piece. In the case of (3), analyzed in Fig. 4, both the target’s standpoint [1.] and the counterargument’s standpoint [2.] are implicit. It should be noted, however, that the mixed confrontation emerging from the counterargument is not between [1.] and [2.]. In this case, [2.] works as an undercutter of the relevance of the premise [1.1] to support the conclusion [1.]. In Rocci (2021: 156) undercutters are analyzed as arguments supporting a (typically implicit) negative standpoint about the inferential connection between premise and conclusion (as in [2.]). Interestingly, in this type of discussion, the other term of the confrontation is not a verbally expressed proposition but rather the inferential connection itself, which can be verbalized as a meta-proposition on the relation between a premise and a conclusion ([1.1] → [1.]).

30While moving in the direction of reconstruction, this diagramming style still aims to be usable for text annotation and to ensure “a direct representation of the contribution of linguistic indicators such as adversatives and concessives” to the structure of the argument (Rocci 2021: 164). It was, in fact, applied precisely to this task in a small-scale study of adversative markers in conversation (Rocci et al. 2020).

31As a workable annotation system for argumentative text, the proposal still has certain significant limitations. Firstly, while it aims at consistently representing a sequential view of counterarguments discussed in 2.2, the system only imperfectly and indirectly preserves the connection between inferential structures and the linear succession of moves in discourse. For instance, the diagram in Fig. 4 allows us to understand that the counterargument [2.1] comes sequentially after the target argument [1.1], as it’s made clear by the attack edge; however, it doesn’t preserve full information on the linear ordering of each unit in the text. For instance, there could be uncertainty as to where the premise [1.1.1 / 2.1.1] occurs in the text, as nothing indicates its initial placement.

32Furthermore, the microstructure of the propositions in the nodes has been manipulated to eliminate ellipses and resolve anaphora. This makes the units less ambiguous but has the side effect of erasing indicators of the sequential placement of the units. Relatedly, the distinction between expressed and implicit standpoints does not emerge from a relation between discourse units and inferential structure but needs to be done with ad hoc means (such as using OVA’s color codes). As we will see in the following sections, these limitations can be overcome by the integration of the IAT and AMT approaches into the proposed IAMT diagramming approach.

3. Toward a combined model for argumentation diagramming

3.1 Inference Anchoring Theory

33Inference anchoring theory (IAT) offers a “scaffolding to represent dialogue and argument structures and the relations between them” (Hautli-Janisz et al., 2022). Fig. 5 shows the IAT representation of the argumentative passage in (4).

(4) You should not eat too much salt. Because it will raise your blood pressure (Example adapted from Budzynska 2013)

Fig. 5: IAT analysis of example (4) (adapted from Budzynska 2013)

34IAT distinguishes between discourse utterances (“locutions”) on the right-hand side of the diagram and their reconstructed propositional contents (“propositions”) on the left-hand side, which exhibit a certain amount of disambiguation, completion, and standardization. While locutions are connected through transitions, representing the sequential structure of discourse and dialogue, on the left-hand side, propositions are connected through edges that specify the inferential and rhetorical relations among them. In Fig. 5 the two propositions are connected through an inference node that connects the premise to its conclusion; here, the nature of the inference node is left unspecified (default inference) – but could be specified by the analyst with a label indicating the argument scheme being invoked. The inference nodes are also important in diagramming complex argumentation to distinguish compound (or linked) arguments, where several premises are linked to a conclusion via a single node, from multiple arguments supporting independently the same conclusion (via separate nodes).

35The two sides of the diagram are connected via illocution nodes. Propositions are anchored to the locutions via illocutions (asserting, in Fig. 5), specifying the speaker’s commitment towards them. Propositional relations (such as inference) are anchored to transitions through the illocutions (arguing in the example), specifying the discourse intention realized by the transition.

36As a particularly sophisticated annotation-oriented theory, IAT has been used extensively in argumentation annotation projects, including very large ones (Visser et al. 2020, Hautli-Janisz et al. 2022). IAT graphs separate propositions from locutions and feature a rich structure to represent the anchoring of inference relations between propositions to sequences of speech acts in dialogue; however, they do not include propositional units that are not anchored to explicit locutionary acts. Thus, IAT lacks a representation of implicit premises and implicit standpoints.

3.1.1. Representing counterarguments with IAT

37We now examine whether standard IAT diagrams can deal with our target examples of concession and counterargument patterns in (2) and (3). As Fig. 6 below shows, despite its richer analytical apparatus, IAT encounters problems that are almost exactly those that we faced using the diagramming style in Peldszus and Stede (2013).

Fig. 6: IAT analysis of example (2) (I Actually Like Teaching on Zoom. There may be less human warmth. But there can be more human connection).

38In Fig. 6, on the right-hand side, we have the three locutions corresponding to the three sentences in example (2), connected through transitions. On the left-hand side, we have the propositional contents and the propositional relations (default inference, default conflict). The propositions are anchored to the locutions via the illocutionary forces they realize: asserting or conceding. This allows us to distinguish between the full commitment associated with assertion and the partial commitment associated with conceded premises. The relations of inference and conflict are anchored to the transitions through the illocutions, respectively, of disagreeing and arguing. Abstracting from the additional structure in the right and central part of the diagram, however, we can observe that the left part is virtually identical to the diagram in Fig. 2, based on Peldszus and Stede (2013). The same critical observations, therefore, apply (see 2.2.).

Fig. 7: IAT analysis of example (3) (If a lecture is only someone talking for an hour, that can indeed be stultifying on video – but that would also be true in a classroom).

39Fig. 7 displays the IAT diagramming of example (3), which we only briefly discussed in relation to the diagramming approach in Peldszus and Stede (2013). The diagram allows us to see more clearly the problem we mentioned in 2.2. Here, the text explicitly conveys an inferential connection which is part of the conceded argument of the majority view; on the other hand, the author’s standpoint is not explicitly stated. Consequently, the perspective is swapped with respect to (2): here, the conceded discourse is represented as drawing an inference, while the author’s argument is represented as a counterargument using an attack (conflict) relation. In short, it turns out that what gets represented as inference or as an attack, in the end, is not a consequence of a perspectival vs. a sequential view of counterargument but simply an unintended consequence of the availability of explicit premise-conclusion connections to the target. In the absence of an explicit standpoint, in Fig. 7 Viet Thanh Nguyen’s asserted counterargument is represented as a rebutter of the conceded conclusion “A lecture can indeed be stultifying on video.”

40This analysis is, however, unsatisfactory: a rebutter is supposed to attack the acceptability of a proposition, but Viet Thanh Nguyen is not saying that it is not true that a lecture can indeed be stultifying on video. He, in fact, concedes that such a proposition could be true if we accept the premise, which he also concedes as a hypothesis for the sake of argument. Looking at the interplay of the illocutionary and the propositional level further reveals the inconsistency of the analysis: one cannot consistently concede the acceptability of a proposition p and assert a proposition q attacking the acceptability of p, and indeed this is not what the author is doing.

3.2. The Argumentum Model of Topics

41The AMT model (Rigotti and Greco 2019) “aims at proposing a coherent and founded approach to the study of argument schemes” (Rigotti and Greco Morasso 2010: 493), aiming to reconstruct the inferential configuration “that underlies the connection between a standpoint and its supporting arguments” (Rigotti and Greco Morasso 2010: 490). Two components are distinguished in the inferential configuration: the procedural one and the material one. The interaction of the two components, giving rise to the so-called Y-structure, is showcased in Fig. 8, again through the reconstruction of example (4).

Fig. 8: Reconstruction of example (4) according to AMT (You should not eat too much salt. Because it will raise your blood pressure)

42The procedural starting points on the right-hand side of the diagram include the locus and the maxim, which can be defined respectively as the semantic-ontological relation on which an argument is based and as an abstract inference warrant that holds, necessarily or presumptively, by virtue of the aforementioned semantic-ontological relation. Each locus can potentially give rise to several different maxims. In Fig. 8 the Aristotelian label “final cause” designates the relationship between goal and action, which generates, among several others, the defeasible maxim “If an action results in undesirable consequences, ceteris paribus, it should not be undertaken.”

43The material-contextual starting points, namely the endoxon and the datum, on the left-hand side of the diagram, interact to derive, in a quasi-syllogistic fashion, a first conclusion to which the maxim can be applied. The endoxon is “a general premise that is accepted by the relevant public in a specific argumentative situation” (Rigotti and Greco 2019); as such, it is often left implicit, being a shared premise already part of the common ground of the interlocutors. The datum is a factual premise, most often corresponding to the propositional content of an explicit argument expressed in the discourse. The first conclusion, derived from the material starting points through the material inference, works as a minor premise in conjunction with the maxim to derive the final conclusion.

44The example illustrates how AMT reconstructs an argument’s “deep” inferential structure, standardizing propositional content and supplementing it with contextual premises, an abstract warrant (maxim), and an intermediate step within the microstructure of inference.

45While AMT has been widely applied in both single-case analyses and small corpus studies, to this date, there is no standardized practice for curating and sharing analyzed examples, nor any publicly available corpus. A clear limitation of AMT in this respect is the lack of a precise built-in mechanism for tracing back the “deep” reconstruction to the sequence of utterances in the surface text. This hinders the development of empirical research aimed at investigating regularities and variations in the relationship between the “deep” inferential configuration and the succession of units in the text. Systematic tracking of text-to-reconstruction mappings could allow the comparison of AMT analyses from different analysts or projects and reveal tendencies and patterns in the relation between discourse patterns and markers and inferential configuration. For an approach such as AMT, where analysts can transform and supplement with relative freedom the original text, such a research, which is currently lacking, is, in fact, vital for testing and refining the AMT theory itself and overcoming the risk of ad hoc, arbitrary and inconsistent reconstruction practices.

3.2.1. AMT diagramming for counterarguments

46While AMT provides a model of the inferential configuration underlying a single enthymeme based on the application of a locus and can diagrammatically combine several Y-structures to represent complex argumentation (Palmieri 2014: 36-42, Rigotti and Greco 2019: 228-241), the model has no standard method for representing the interaction of an inference with a counterargument.

47Palmieri and Musi (2020) have to deal with this limitation in a case study on a public controversy when they try to elucidate which parts of the inferential configuration of the target argument are hit by the observed counterarguments. While the target is represented as a fully-fledged Y-structure, counterarguments are not analyzed as Y-structures of their own, but just as “attacks” hitting on certain parts of the inference (see Palmieri and Musi 2020: 285). Let us apply this approach, further developed in Palmieri (2024), to our example (2).

Fig. 9: Actual and potential counterarguments to the inferential configuration of (2), following Palmieri (2024). The attested counterargument (counter-standpoint) appears in black print, potential counterarguments appear in blue print.

48According to Palmieri (2024), a counterargument can work by attacking four different components of the inferential configuration of an argument displayed by a Y-structure. It can simply present an argument of the opposite conclusion; in this case, it is called a counter-standpoint and interacts only with the final conclusion of the Y-structure. Palmieri (2024) identifies this possibility with the rebutter of the conclusion. It can function as an attack on the acceptability of the datum, which corresponds to the notion of rebutter of the premise. Finally, undercutters are divided into two separate categories. An opponent can attack the relevance of the explicit argument by pointing out that the presupposed endoxon is, in fact, questionable or even outright false (for instance, a false authority in the case of the argument from authority). A different kind of undercutter occurs, according to Palmieri (2024), when the sufficiency of the argument is attacked by exploiting the conditions of exception of a defeasible maxim (for instance, by pointing to unintended negative side-effects in the case of practical argumentation).

49As Palmieri (2024) contends, the possibility of tracing back different types of attacks to different components of the target inference holds considerable promise for refining the reconstruction and evaluation of counterarguments. The diagramming practices of AMT, however, struggle to support this kind of analysis. As a matter of fact, the representation is asymmetric: while the target argument is a fully-fledged Y-structure, the counterargument is represented as a simple attack rather than as an inferential configuration of its own.

3.3. Anchoring enthymemes to discourse with IAMT

50These limitations can be overcome by combining AMT with IAT in the proposed IAMT analytical model. IAMT allows us to represent the enthymematic argumentative structure of a counterargument and relate its explicit and implicit parts to the dynamic development of a discourse and to the perspectives of the participants. Fig. 10 below provides the fully fledged IAMT diagram of example (3).

51IAMT diagrams integrate the AMT inferential configuration on top of the basic IAT annotation, whose main elements are maintained. By doing so, IAMT zooms in onto the inferences anchored to the transitions, supplying the implicit premises and warrants that the inference requires. These are diagrammed as propositions that are anchored not to locutions but rather to transitions via ad hoc illocutions; endoxa and maxims are presupposed by the act of arguing, while intermediate conclusions and implicit final conclusions are anchored by an illocution of the implying type.

Fig. 10: IAMT analysis of example (2). [The OVA map of this analysis is available online at https://www.aifdb.org/​argview/​33255 (select “Edit with OVA+” on the top right menu)].

52The left-hand side of the IAMT diagram displays two full inferential configurations, exact translations of the corresponding Y-structure diagrams. The material inference derived from the endoxon and datum is depicted as a default inference node, while the topical inference stemming from the maxim and the intermediate conclusion is marked by an inference node bearing the label of the invoked locus. In this case, both the conceded argument and its counter are based on the locus from the final cause and invoke similar maxims. Since this is a case of rebutter of the conclusion, the two inferential configurations are joined by a default conflict node at the level of their final conclusions, representing a dialectical confrontation. The direction of the conflict edge goes from the explicit standpoint of the counter (I Actually Like Teaching on Zoom) to the reconstructed target standpoint attributed to the concessively evoked “majority view.” This reflects the intended sequentiality of the concession and counterargument pattern and accounts for the contribution of the adverb “actually.” Since IAMT diagrams can be daunting at first sight and a modicum of exposure is required to train the eye to discern their structure, it is useful to zoom in on the part of the diagram encoding the conceded inferential configuration using the color-coded version of the diagram in Fig. 11.

Fig. 11: Detail of the conceded argument in (3). Attested locutions and corresponding proposition nodes are in light blue, inference nodes in green, the conflict node is in red, illocutionary nodes in yellow and transitions in purple. The thick dotted line highlights the inferential configuration (Y-structure equivalent) of the conceded argument.

53While all the information of the IAT and AMT analyses is retained, new facts become observable and, most importantly, adequately recordable in the new style of analysis. If we look at the correspondence between the inferential configuration and the sequential structure of the text, we can observe that the two inferential configurations are intertwined. The first locution introduces the final conclusion of the counterargument, indicating its contrarian nature with a signal of expectation denial (“actually”). The conceded datum of the majority argument follows as the only direct manifestation of the conceded argument. The final locutions present the datum of the counterargument supporting the explicit standpoint through the second inferential configuration. For this reason, the diagram presents the second inferential configuration almost upside-down, with its final conclusion at the outset of our little discourse sequence.

54From an inferential viewpoint, we can observe that the two inferential configurations, so to say, meet only at the top of their final conclusions. Following Palmieri (2024), we have read the rebuttal of the conclusion essentially as a counter-standpoint. This raises interesting questions. How does a counter-standpoint meet its burden of defeating the existing argument? If we look at the inferential configuration of the two arguments, however, we see that they are not entirely independent: they exploit the same locus with converse maxims while appealing to different but comparable endoxa. Clearly, the arguer does not openly engage in an undercutter of the sufficiency of the conceded argument, yet the parallelism may hint at it: it is not sufficient to only consider one kind of positive effect.

55The complete IAMT representation of example (3) involves no less than four inferential configurations, as can be gleaned from the more straightforward reconstruction in Fig. 8. For the sake of clarity, we present in Fig. 12 an abridged version, where only the inferential configurations of the undercut and undercutting inferences are fully spelled out in IAMT.

Fig. 12: IAMT analysis of example (3). The thick dotted line highlights the inferential configuration (Y-structure equivalent) of the conceded argument. [The OVA map of this analysis is available online at https://www.aifdb.org/​argview/​33256 (select “Edit with OVA+” on the top right menu)].

56In example (3), we have a clear example of an undercutter of the sufficiency of the conceded argument. The IAMT diagram maps it as an inference based on the locus from alternatives – a locus typically encountered in association with the locus from the final cause, whose conclusion conflicts with the maxim of the undercut argument, which is deemed insufficient to warrant the conclusion.

Conclusion

57In this paper we have explored the strengths and limitations of annotation-oriented and reconstruction-oriented argumentation diagramming methods for mapping counterarguments, with special attention to concession and counterargument patterns in monological discourse. In particular, we sought to highlight the complementary strengths and limitations of IAT and AMT, building a case for their integration in a combined diagrammatic style. In the last part of the article we presented and applied a first sketch of IAMT as a combined method.

58The approach is clearly still in its infancy and requires refinement through application to a varied set of authentic examples. It is also clearly a high-resolution, very detailed style of analysis whose applicability is limited to collections of short argumentative passages extracted from a larger corpus for in-depth analysis.

  • 4 The IAMT analyses of examples (3) and (4) are retrievable from the AIFdb repository, respectively, (...)

59Notwithstanding these limitations, IAMT represents the first approach to the standardized coding of AMT-style analyses in a formalized, machine-readable, language based on the Argument Interchange Format and the OVA platform for argument visualization, allowing the storage4, retrieval and comparison of passages analyzed for their inferential configuration, and the creation of growing collections of comparable examples targeting specific loci, specific rhetorical and argumentative patterns, specific linguistic discourse markers, or argumentative indicators. This seems a promising development for the empirical study of argument schemes in interaction with micro-discursive phenomena in the AMT theoretical perspective.

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Notes

1 As an acronym, the label IAMT might be read as Inference Anchoring Model of Topics. But, in fact, the label IAMT was born more as a playful portmanteau blend of IAT and AMT – the acronyms of the parent theories - than as real, meaningful, acronym.

2 The terms “implicated premise” and “implicated conclusion” originate from Relevance Theory (Sperber and Wilson 1995).

3 Although OVA was designed from the outset to apply the IAT framework (detailed in section 3), it can be used to realize a variety of diagramming approaches and can be implemented with labels derived from various theories. For instance, in the following pages, we will employ OVA’s general diagramming capabilities to represent the diagrams applying the approaches from Peldszus and Stede’s (2013) and Rocci (2021). We will also use OVA for representing IAMT diagrams, employing the basic IAT features and labels and enriching them with ad hoc complements.

4 The IAMT analyses of examples (3) and (4) are retrievable from the AIFdb repository, respectively, at the following URLs: https://www.aifdb.org/argview/32020 and https://www.aifdb.org/argview/32021. In order to correctly visualize the analysis select the option “Edit with OVA+” in the menu on the upper right corner of the window.

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Référence électronique

Andrea Rocci et Costanza Lucchini, « Diagramming the Enthymematic Structure of Counterarguments. An Introduction to IAMT Diagrams »Argumentation et Analyse du Discours [En ligne], 34 | 2025, mis en ligne le 10 avril 2025, consulté le 21 avril 2025. URL : http://journals.openedition.org/aad/9212 ; DOI : https://doi.org/10.4000/13q0e

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Auteurs

Andrea Rocci

USI Università della Svizzera italiana (Switzerland)

Costanza Lucchini

USI Università della Svizzera italiana (Switzerland)

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