Finding enthymemes in real-world texts: A feasibility study

2.1.Enthymematic syllogisms

All types of arguments can be expressed in a truncated form, but truncated syllogisms are the most studied types of these [7]. Standard-form syllogisms are convenient for the analysis of enthymemes, because such arguments consist of only three terms and satisfy a set of strict requirements. These requirements uniquely define the form and the order of argumentative propositions and terms [36]. Therefore, given any two syllogistic propositions, the goal of restoring the missing premise or conclusion can be achieved by following a set of deterministic steps. For instance, consider the enthymeme below:

As can be inferred from the formal definition of a syllogism, this is a categorical syllogism with the minor premise and the conclusion expressed. There exists a general procedure [7] that allows us to conclude that the missing proposition is:

The procedure for restoring the missing proposition is the following:

In this way, enthymematic syllogisms allow for a straight-forward and objective definition of the missing proposition: they already physically contain all three terms required for the reconstruction, so that no external information is necessary. This means that the process of reconstructing syllogistic enthymemes can potentially be automated. However, it is almost impossible to find well-formed standard syllogisms in everyday language, as we shall see later.

2.2.Enthymemes in everyday language

Unlike syllogisms, the majority of arguments used in natural language discourses are not formed from a set of structurally pre-defined propositions. Instead, people use a set of reasons to support their claims [29]. These reasons can be non-defeasible, i.e. universally true, or defeasible, i.e. they can be defeated by some new information [25,28]. The propositions left implicit in enthymemes are often defeasible, because the speakers prefer not to state potentially weak reasons explicitly [45]. For example:

The missing proposition here, all lawyers do not know about differential equations, is clearly not universally true.

Information attacking defeasible reasons is called defeater. There exist two types of defeaters, undercuts and rebuttals. The undercutting defeater attacks the connection that exists between the reason and the conclusion, while the rebutting one attacks the conclusion itself. For example, recall the enthymeme mentioned in Example (2). It can be attacked by both the undercut, Penguins are also birds, but they do not fly, and the rebuttal, But tweety is too heavy to fly.

Due to the defeasible nature of argumentative claims used in everyday language, formal notations, such as syllogistic logic, cannot be applied for the restoration of naturally occurring enthymemes [10]. For instance, Campbell [4] argues that the majority of Darwin’s claims cannot be expressed through logical arguments. The mechanical approach of reconstructing enthymemes in such a way that they become structurally correct and include the needed assumptions may lead to incorrect interpretations of an argument, i.e. to the insertion of premises not intended by the speaker. In Example (2), All birds fly exemplifies this problem. The statement intended by the speaker might be defeasible: Generally, birds fly. Therefore, our attempt to convert the statement into a well-formed syllogism by means of the universal quantifier results in an incorrect statement.

Implicit argumentative propositions are not always defeasible. Some of them represent universally true facts that are too trivial to be stated explicitly [18]. This observation is captured by Grice’s Maxim of Quantity – Do not make your contribution more informative than is required [16]. This pragmatic principle discourages a speaker from making explicit statement of facts that are widely accepted by the audience; in fact, the explicit statement of such facts would sound both trivial and also unnatural to a listener. This is another reason why enthymemes are so frequent in natural language discourses.

Jackson and Jacobs [19] notice that enthymemes also play an important role in maximizing a listener’s agreement, because additional information may contain a subjective point of view and increase the possibility of disagreement. For example:

The missing proposition in this humorous argument, Wagner composed music while having no ideas whatsoever, is subjective, and many people will disagree with it. The author therefore refrained from stating it explicitly.

The detection of hidden and implicitly stated arguments is much harder than the treatment necessary for enthymematic syllogisms; it would require a thorough analysis of argumentative structures and strong general or domain-specific knowledge. The question of how much domain knowledge is needed becomes particularly critical when enthymemes appear in scientific domains; their resolution is therefore usually reviewed as an activity for experts in the area [4]. Crick states that enthymemes are frequent in scientific writing, as a result of the fact that the audience is assumed to consist of experts in the field [8]. Enthymemes make scientific persuasion more engaging and initiate cognitive cooperation between the writer and the audience, hence creating a stronger persuasion effect than if complete arguments had been used, which may be initially surprising. According to Campbell, the effect is achieved by the shared reasoning process between writer and audience, where missing premises are jointly filled in [4]. Because of their persuasive power, Aristotle called enthymemes “the strongest of rhetorical proofs”.

As can be seen from the reasons that explain the occurrence of enthymemes in everyday language, the task of restoring the assumptions intended by the speaker is an unfeasibly challenging task, particularly if one does not have access to the formal structure of the argument. It relies on general knowledge and on subjective interpretation of an enthymeme, given the unlimited number of choices and humans’ viewpoints [10]. Moreover, it is not clear how many assumptions should be inserted in order to make the argument complete. Therefore, our solution relies on a fixed argumentation strategy, thereby carefully restraining the theoretically possibly unlimited choice. As a result, we do not require a fully mechanical procedure for enthymeme reconstruction.

3.1.Kienpointner’s scheme and extension

Kienpointner [20] designed the following argumentation scheme for a minore ad maius arguments:

We formulate the equivalent scheme for a maiore ad minus:

Our observation is that while this scheme is correct and explanatory, it does not express the additional implicit scaling relation that holds between X and Y. Consider the following example:

Kienpointer’s scheme only allows expressing:

As can be seen, the suggested insertion does not explain the key scaling relation size between X and Y:

To address this problem, we extend Kienpointer’s argumentation scheme with a fourth proposition that describes a concrete relation holding between X and Y:

The relation R between X and Y is almost always implicit, which makes a fortiori arguments ideal cases for our investigation of the feasibility of reaching agreement in an enthymeme interpretation task.

3.2.Nedum and let alone sentences

A fortiori arguments can be expressed in natural language by many linguistic constructions, involving for instance of course, not...even, and if...then.

In this study, we investigate one of the most typical a fortiori constructions: let alone sentences. Let alone is a convenient a fortiori construction, because all the necessary components are usually present in a single sentence, and the amount of argument-irrelevant information in that sentence is minimal. Consider Example (5) paraphrased for let alone construction:

Let alone is a nedum – a connective particle that signalizes that the second clause of the construction is more relevant to the context and can be inferred from the first clause [33]. For example:

According to Fillmore et al. [13], let alone can be syntactically treated as a coordinating conjunction, where the phrases linked by let alone display parallelism with respect to grammatical functions, e.g. direct object (adult and child) or verbal complement to auxiliary (sit and walk). In the terminology of Toosarvandani [42], the stressed elements in the first and second part of the sentence are called correlate and remnant respectively.

Let alone can be used to signal both positive and negative a fortiori arguments, representing a minore ad maius and a maiore ad minus arguments respectively. Sawada [31] distinguishes the following three main cases of let alone arguments: explicit negative (Example (12)), implicit negative (Example (13)), and explicit positive (Example (14)):

Toosarvandani [42] observes that some form of scaling information is always present between the remnant and the correlate, making the correlate in some respect more likely for negative sentences and less likely for positive ones. The hearer can pragmatically infer, based on common knowledge [16,35], that these stressed elements are ordered based on some scale. This hidden scalar reasoning is highly relevant to our task of finding arguments with hidden premises, and is captured in the extension to Kienpointner’s scheme presented in Section 3.1 above. We argue that let alone sentences are by definition enthymemes, and that the missing scalar relation, called relation R above, is an important part of the missing proposition necessary for the conclusion to be accepted. The conclusion is therefore always a statement about the remnant, which is entailed from both the parallel statement about the correlate and the inserted scalar relation.

4.1.Category definition

1. Part of: The relationship between the referents in remnant and correlate is that of superset. For example:

The scaling relation R here is: Germany is a part of Europe.

This relation has a number of requirements:

This case is not covered here, but in the category called Additional constraint.

2. Smaller than: The scale concerned involves cardinalities or standard measurements which connect the remnant and the correlate. For example:

The scaling relations here would be:

Such arguments compare measurements of the correlate and remnant’s properties (e.g., weight, age, volume). In an Example (18), the scalar comparison is between the volumes of a bottle of water and a saucepan:

However, in order to make the annotation task more straightforward, we omit the obligatory mention of the property and accept direct scalar comparisons between the remnant and the correlate.

3. Precondition: The action in the remnant necessarily requires the action in the correlate having taken place earlier. For example:

The scaling relation here would be: participating is a precondition for winning.

Fellbaum [11] presents four types of entailment relations between verbs; our precondition corresponds to her backward presupposition (winning presupposes participating).

4. Other lexical entailment: This relation covers the larger class of actions where the proposition expressed in the remnant lexically entails the proposition expressed in the correlate. There can be temporal overlap between the two propositions, unlike in category 3, where the proposition in the correlate has to be completed before the proposition in remnant can begin.33 For example:

The scaling relation here would be: snoring entails sleeping. Snoring can only happen during sleeping. Additionally, snoring and sleeping can occur simultaneously for some of the time, but it is not necessary that snoring entirely overlaps with sleeping; there can be times of sleeping without snoring.

5. Earlier date: This is a special case of Smaller than category, where the property is time: in the case of irreversible events, if a state becomes true at time t0 for the first time, by definition it does not hold at any earlier time t<t0. This relation relies on the uni-directionality of this particular scale, time. For example:

The scaling relation here would be: 1909 is an earlier date than 1923.

6. Additional constraint: In his category, a number of semantic predicates (constraints) applied to the correlate are compared to the same set of predicates plus additional predicates in the remnant. For example:

Here, a middle-aged prince is a double-constraint on a person, which filters out some middle-aged non-princes.

7. Additional referents: This category covers cases where the set of referents in the remnant logically includes the referent from the correlate. For example:

It is hard to imagine a company that would insure the family of an employee without also insuring the employee himself. The intended meaning of the remnant must therefore be logically interpreted as “the employee and his family”.

8. Cumulative/independent: Here, the remnant of let alone is not directly comparable to the correlate, but becomes interpretable if we read it as an additive constraint. For example:

Here, both the feature of protecting the contents and of being decorated with Easter motives are important for Easter egg packaging. The intended meaning that speaker put into this argument is:

Hence, the combination of the two qualities of the Easter-egg packaging is compared to the quality of protecting its contents. One possible test for whether the relation is independent/cumulative is to try to substitute let alone with in addition to. If the meaning does not change, then the remnant and the correlate are likely to be in the independent/cumulative relation.

The three categories Easier than, Less likely than, and More extreme case than are fallback options, which are only to be used if none of the more specific categories applies. For example:

4.2.Linguistic templates

There is a connection between the scale category introduced in the previous section and the linguistic form of premise that can be constructed from that class, as can be seen from Table 2.

Each scaling relation is represented by one template out of the many possible verbalizations of that relation. Annotators were asked to extract the appropriate parts from the given sentence and insert them into the template of their chosen category. For instance, for Examples (15)–(27) they were expected to write the sentences in Table 3. (Material directly excised from the sentence is shown in boldface.)

As can be seen from these examples, some of the statements thus constructed are always true, such as: Snoring lexically entails sleeping, Germany is a part of Europe or participating is a precondition for winning. However, some of the statements are true only in the given context. For example, The distance to New York is smaller than the distance to the West Coast holds only for certain speaker locations. Nevertheless, such statements can be good candidates if our aim is to represent knowledge about generally accepted facts.

5.1.Enthymeme classification task and results

Two annotators (the authors of this paper) made a binary decision when faced with a let alone sentence; they had to decide whether the sentence contained enough context to interpret the sentence and to restore the missing statement. They additionally crossed out any information that was not relevant to the argument expressed in the let alone sentence, or actively distracting.

The number of positive choices was high (183 out of 200). The inter-rater agreement was calculated by means of Cohen’s kappa statistics [5], to be K=0.729 (N=100, k=2, n=2). We use Cohen’s standard formula:

There were only 2 out of 183 cases where either annotator specified enthymeme-irrelevant information, namely:

5.2.Enthymeme classification task

The next stage of the experiment is performed only on those let alone sentences that were positively classified by both annotators as enthymematic (90 cases).

The annotators classified the let alone sentences according to the annotation scheme from Table 1 in order to describe the scale that applies for the a fortiori argument.

The agreement between annotators was K=0.75 (k=2, n=2, N=90). This indicates that annotators were overall well able to distinguish scaling relation categories.

The class distribution per category is skewed, as can be seen in Table 4. The most frequently chosen category was the “precondition for” relation – 61 cases (33.9%). The “additional constraint” and “additional referent” classes were also frequent (12.7% and 10% respectively). The fact that the fallback categories were chosen relatively frequently suggests that there are cases where the context is not enough to disambiguate the scale.

The small sample size prevents us from analyzing problematic categories systematically, but we noticed that earlier date and precondition for seem to be relatively harder for the annotators to distinguish reliably. Despite the very distinctive nature of the “cumulative/independent” category, the annotators frequently disagreed on this relation type. We believe that most of the disagreements for the fallback categories came from the fact that one of the annotators preferred these generic relations to more specific ones. For example:

While one of the annotators classified this relation as a strike is smaller than a revolution, the second participant preferred the easier than category (a strike is easier than a revolution).

While such unclear cases are in the nature of annotating subjective interpretative phenomena, the relatively high agreement we observe means that overall they are rare.

5.3.Enthymeme reformulation task

The annotators next composed a new sentence expressing the missing premise, using the textual material extracted from the given sentence together with the template for the chosen category, as described in Section 4. The 71 cases where the annotators previously agreed on the chosen scale category were used for this measurement.

We report the percentage of identical or near-identical statements. Judgments of what is identical were made by the first author, but they were very strict, allowing variation only with respect to near-synonyms or the addition or omission of non-relevant information.

69 premises (97%) were judged to be identical or near-identical.

Only two disagreements occurred, the first of which was:

While both annotators identified that “questioning” is a precondition for “providing an analytical basis to justify”, they specified partially different propositions:

(a) Questioning something is a precondition for providing an analytical basis to justify something.

(b) Questioning classical macroeconomics is a precondition for providing an analytical basis to justify classical macroeconomics.

The second enthymeme on which the annotators disagreed was:

Here, the annotators disagreed on the ellipsis resolution:

(a) For Wimbledon, to be an English force is easier than to be a European force.

(b) To be an English force is easier than to be a European force.

Overall, two disagreement cases out of 71 is a surprisingly low number, given that we demanded linguistic descriptions of quite complex pragmatic effects, and given that the annotators, while knowing the scheme and the ideas, were still working entirely independently on a task that was hitherto deemed too unrestricted to be done at all. The pilot experiment in our opinion shows that applying the right kind of restriction can result in an objective definition of truth, even in seemingly open-ended situations.