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We propose a revised definition of “argument scheme” that focuses on describing argumentative performances and normative assessments that occur within an argumentative context, the social context in which the scheme arises. Our premise-and-conclusion structure identifies the typical instantiation of an argument in the argumentative context, and our critical framework describes a set of normative assessments available to participants in the context, what we call practically normative assessments. We distinguish this practical normativity from the rationally or universally normative assessment that might be imposed from outside the argumen-tative context. Thus, the practical norms represented in an argument scheme may still be subject to rational critique, and the scheme avoids the is/ought fallacy. We ground our theoretical discussion and observations in an empirical study of US district court opinions resolving legal questions about copyright fair use and the law-yers’ briefs that led to them, instantiating our definition of argument scheme in the “argument for classification by precedent.” Our definition addresses some criticisms the argument-scheme construct has received. For example, using our data, we show that a minimally well formed instance of this type of argument does not shift any conventional burden from the proponent of the argument to its skeptics. We also argue that these argument schemes need not be seen as dialogical.


Introduction
This special issue calls for exploring the norms of public argumentation. We consider American judicial arguments to address issues of normativity in Waltonian argumentation schemes (Walton et al. 2008). In common-law countries like 1 3 the United States, written opinions of judges applying the law become primary authority for future judges applying the same or similar laws. American lawyers submit argumentation that becomes part of the public record, in which they cite legal authorities, including prior court opinions or "precedents," to support claims about applicable legal standards or rules in an instant case. A lawyer's goal is to persuade a judge to attach a legal classification and its attendant consequences to a party, e.g. "the defendant is liable in negligence to the plaintiff." Consequently, these lawyers and judges engage in "public argumentation" because their arguments "address[] a large[] audience" of other lawyers and judges "in their public capacity... about a public issue," and their status as public records makes the court an "open forum" (Zenker et al. 2019, p. 4).
We propose a revised definition of "argument scheme" that focuses on describing argumentative performances and normative assessments that occur within this argumentative context. Our premise-and-conclusion structure identifies the typical instantiation of an argument. Our critical framework describes the set of normative assessments that participants in the argumentative context may perform, what we call practically normative assessments. We distinguish this practical normativity from the rationally or universally normative assessment that might be imposed from outside the argumentative context. Our scheme thus focuses on what theorists commonly refer to as "appropriateness standards prevailing in the exchange concerned" (van Eemeren et al. 2014, p. 6), and "premises... acceptable to the audience" (Govier 1999, p. 119), etc. But some premises acceptable and "sufficient to warrant belief in [a] conclusion" (Govier 1999, p. 119) within the argumentative context may not be acceptable at a universally normative level, and the argumentative context may not permit others that would be relevant from the universally normative perspective. We thus address the transference of "the acceptability of the premises to the conclusion" (Hansen 2021, p. 208) or increasing the "the adherence of the minds addressed" to the conclusion based on the argument (Perelman & Olbrechts-Tyteca 1969, p. 6), but only within the constraints of the argumentative context.
Consequently, any instantiation of our definition of argument scheme is subject to criticism by theorists on two grounds: First, whether it accurately describes the argumentative behavior of participants in the argumentative context, including whether it describes the normative bases of assessment they do use; and second, whether the normative bases of assessment they do use are those that they should use. The former is a descriptive question and the latter a normative one, or perhaps a "meta-normative" one, in that it relates to norms about norms (Larson 2021). We contend that the failure to recognize these two levels of normativity has caused confusions in the literature surrounding argument schemes.
We recognize that our approach may seem a radical departure from that of Walton et al. (2008). Though we believe that we do not so much break from prior work as to clarify it, we have insufficient space here to support all our revisions with complete arguments. Further theoretical and empirical work will be necessary to fully explore what we have proposed. Toward that end, we report on an empirical study to determine whether judges and other lawyers accept a lawyer's use of what has sometimes been called a "legal analogy" without articulating a deductive "covering rule" (Larson 2019;Brewer 1996Brewer , 2018Weinreb 2016), what we call "unruly analogies." Before we could answer our research question about unruly analogies, we needed to clarify what an argument(ation) 1 scheme is and how it works, at least in this empirical context, and to resolve some issues that scholars have raised regarding schemes. Section 2 discusses those issues and offers our proposed definition of "argument scheme." Section 3 discusses our empirical study and its context. In Sect. 4 we instantiate our definition of argument scheme as the "argument for classification by precedent" and discuss implications of our approach to some open questions in argument-scheme theory. Section 5 proposes future research.

Argument Schemes and Their Challenges
What exactly an argument scheme is and does has been subject to considerable discussion since well before the publication of the oft-cited Walton et al. (2008) compendium of schemes. Following Walton et al., we take the three key functions of argument schemes to be to "represent structures of common types of arguments....", to "enable one to identify" them, and to enable one to evaluate them (p. 10-11). Consider the example of Walton et al.'s Argument from Analogy: Version 2 (p. 58): Major Premise: Generally, case C 1 is similar to case C 2 . Relevant Similarity Premise: The similarly between C 1 and C 2 observed so far is relevant to the further similarity that is in question [proposition A]. Minor Premise: Proposition A is true . . . 2 in case C 1 . Conclusion: Proposition A is true . . . in case C 2 . Walton et al. (2008, p, 62) also supplies a set of "critical questions" (CQs) associated with this scheme: CQ1: Is A true . . . in C 1 ? CQ2: Are C 1 and C 2 similar, in the respects cited? CQ3: Are there important differences . . . between C 1 and C 2 ? CQ4: Is there some other case C 3 that is also similar to C 1 except that A is false . . . in C 3 ?
Walton et al.'s formulation raises several questions, but a central one that influences answers to the others is whether schemes should be seen as descriptive or normative.

Descriptive or Normative, and Other Issues
Some scholars appear to hold that argument schemes should be normative to earn any credibility as presumptive argument forms or as shifting an argumentative burden to the receiver (Becker 2016;Lumer 2022). Others acknowledge the need for the schemes to represent the experiences or expectations of the people making the arguments (Becker 2016;Shecaira 2016). There might be a tendency to see the critical questions associated with a scheme as the normative part of the framework, but their status is not so clear. Walton et al. (2008) sometimes seem to separate them from the scheme, speaking of CQs "matching" the scheme (pp. 9, 11) or coming after the argument in a dialogical context (p. 3). At other times, they imply that they are one. To other scholars, the CQs sometimes appear a supplement to the argument scheme (Godden & Walton 2007a, b;Hansen 2021;Shecaira 2016;Yu & Zenker 2020), and sometimes they appear integral (Baumtrog 2021;Becker 2016).
For many scholars, critical questions play a normative role (e.g. Baumtrog 2021;Hansen 2021;Lumer 2022;Yu & Zenker 2020), but on the Waltonian account, they need not. Whether a CQ is part of the scheme or stands alongside it, it seems apparent that its "legitimacy... derives from the fact that it tests some aspect of its target argument against" normative criteria (Godden & Walton 2007a, b, p 277-278). Becker (2016, pp. 27-28) suggests the following purposes for CQs: expressing implicit premises, checking premises, checking "the reliability of information sources," clarifying "vague expressions," and assessing whether the argument advances the discourse toward a resolution. Becker's view is not inconsistent, however, with viewing the CQs as descriptive, as merely "typical or common way [s] in which an argument of a certain schematic type can fail to meet" normative criteria (Godden & Walton 2007a, b, p. 282). Unfortunately, a descriptive account of CQs might leave out much that might be useful for assessment if certain questions are not asked frequently or typically.
Deciding which issues the premises address and which the CQs address is also a matter of debate that seems tied up with the descriptive/normative divide. Walton et al. are noncommittal, claiming that incorporating all the CQs into the premises "would work as well as" their approach, that it "doesn't really matter that much which version you use," but that their approach "strikes a nice balance" (p. 20). Walton et al.'s (2008) CQs seem sometimes to test all the premises, sometimes only some, sometimes to include most of the other issues necessary to make the scheme normative, and sometimes not. Lumer (2020, p. 241) has described Waltonian schemes as highly enthymematic and claims "[c]omplete arguments [would] contain all premises necessary for conclusiveness..." At a minimum, he argues that "the critical questions about the enthymemtatic schemes should at least also contain critical questions about the truth of the premises to be supplemented..." (p. 244). But where the CQs ask for confirmation of the expressed premises, he says "these critical questions do not add anything new" (p. 254), suggesting that repeating these premises in the CQs lacks value. Hansen (2021) claims that a normative scheme will have more premises, and Baumtrog (2021) too prefers a proliferation of premises that CQs would then test. Shecaira (2016, p. 512), however, warns against too much supplementation of premises in the scheme, reconstruction that may result in over-application of the "principle of charity" (see also Hinton 2021). "A normative scheme" cannot do its work "by proposing adjustments so profound that they render the argument type unrecognizable" (Shecaira 2016, p. 517); it should instead meet a standard of "minimal descriptive adequacy" (p. 508). 3 In other words, theorists must not multiply premises to satisfy normative goals if they thereby defeat descriptive goals.
We believe addressing the normative/descriptive divide could help resolve many other questions. Nevertheless, a simple division between descriptive and normative does not capture all that we seek from argument schemes, in part because it fails to acknowledge the different bases for argument assessment available to participants within an argumentative context and to those outside it.

"Argument Scheme" Defined
We offer the following definition of "argument scheme" for discussion in this section, describe an application of it to an empirical study in Sect. 3, and discuss implications of our findings in Sect. 4.
AS is an argument scheme if and only if AS comprises an argumentative context AC, a premise-conclusion structure PCS, and a critical framework CF.
AC is a community of persons or a specific social activity where there exist "situationally appropriate responses to recurrent [social] situations" (Berkenkotter & Huckin 1994, p. ix).

PCS comprises:
• A conclusion C, a sentential form which expresses a proposition. 4 • The sentential forms Prem 5 necessary in AC to identify an argument of the type represented by the scheme that provides support for C.
CF is a set of propositional forms Prop that includes the propositions expressed by Prem and that collectively gives the most cogent possible argument 6 for the acceptability of C in AC.

3
Note an important distinction between PCS and CF: An instantiation of PCS's sentential forms results in linguistic performances, utterances; 7 an instantiation of CF's propositional forms results in "objects of belief," propositions (McGrath & Frank 2020). Section 2.3 discusses some ways in which our proposed definition might address issues in Sect. 2.1.

Descriptive and (One Kind of) Normative
Our approach to argument schemes is largely descriptive and depends heavily on defining the argumentative context AC both for determining contents of the premises in Prem and the propositions in the critical framework CF. The normativity that CF offers is for participants within the AC, what we call "practical normativity." Whether those norms are satisfactory on any universal level is a question for the researcher looking into the AC from outside. 8 We start from the concept of the argumentative context AC because every scheme assumes a context of use (Becker 2016). While Walton et al. (2008) describe argument schemes as forms of "common types of arguments used in everyday discourse" (p. 10, emphasis added), they nevertheless discuss types of arguments likely to arise in particular contexts and give examples especially from legal contexts. But the practices of argument proponents in different contexts vary, as do the available norms for assessing arguments. Consider the mathematical proof, where deductive closure is required 9 ; the argument of a biologist for a causal connection between variables, where statistical inductive argument may prevail; and the lawyer's argument about whether a judge should grant a certain form of legal relief, where legal analogy is common. The extent to which the argument proponent must express premises and the types of critical response an audience can bring to bear differ in each context. Thus, practically normative characteristics of a scheme-those in use by actual participants in the AC-are bounded in some ways by AC.
Next, we propose a clear division of labor between the premise-and-conclusion structure PCS and the critical framework CF. The PCS serves as a description of sentential forms argument proponents typically utter when instantiating an argument of this type. In this way, the scheme functions to represent the forms of and identify the type of argument (Walton et al. 2008) and responds to Shecaira (2016) and Hinton's (2021) admonitions that we should not supplement schemes to the point where they are unrecognizable to those making the arguments in the AC. The CF serves a normative function, providing a broader set of propositional forms that would, if truthfully asserted, make the argument as cogent as possible within AC. But as Baumtrog (2021, p. 632) noted, the "normative is never fully normative" and "the descriptive is never fully descriptive.". In Walton's conception of the argument scheme, an argument proponent instantiates the premises and conclusion, which together make the argument presumptively acceptable and shift a conventional argumentative burden to an interlocutor to respond with questions. Here, the PCS is descriptive and may depend on social conventions and pragmatic constraints. Identifying such an argument means taking its form as evidence about what the proponent means it to do within those constraints. We intend this to refer to the common acceptance of the argument type, rather than ad hoc acceptance by the participants in a particular argumentative or dialectical exchange (c.f. van Laar 2011, p. 349, "commonly adopted argumentation scheme"). It is not merely descriptive, however, because it serves a rhetorically normative function (Shecaira 2016): If an argument proponent instantiates an argument scheme without including the sentential forms in the PCS-or if they include superfluous sentential forms-the audience might not recognize the argument type or might sustain a heavier cognitive load when parsing the argument, potentially making it less effective. 10 There are thus practical norms-norms imposed by the AC-that influence the form of the PCS.
While the existing literature is not univocal on the matter, we believe that critical questions or the critical framework CF should exhaust the issues that are relevant for testing the sufficiency of the claim within AC. The constraints of AC are important for this formulation of CF, because every scheme assumes a context of use (Becker 2016) and "[o]our schemes should be tailored to the specific phenomena we are analyzing" (Shecaira 2016, p. 515). Consequently, not all possible propositions that could rationally support C will be acceptable in all ACs, and not all the propositions in Prop would rationally support C in other ACs. For example, the US Federal Rule of Evidence 403 permits a court to exclude evidence that would be probative regarding a standpoint if the evidence would unfairly prejudice the jury regarding a party. A normative system that is context-independent-one normative according to some universal standard (see Baumtrog 2021; Shecaira 2016)-would not exclude such evidence. 11 Thus, in our model, the CF includes all the propositional forms that are normatively accepted in the AC, but it does not include all propositional forms that might rationally enhance the cogency of the argument. Consequently, the normativity of this argument scheme is a practical normativity; that is, it represents the dialectical norms of the participants in AC. Of course, this does not prevent argumentation theorists from exercising "meta-normativity," as we called it in Sect. 1, where they would criticize the practical norms within a given community of argument proponents or a given argumentative context. Subject to that limitation, the complete list of propositional forms in CF allows the argument scheme to serve its evaluative function and satisfies the expectations of theorists such as Lumer (2020), 1 3 Baumtrog (2021), and Hansen (2021) that the scheme should provide a complete evaluative framework.
Our empirical study of a particular argument scheme-the argument for classification by precedent in American judicial arguments-which we describe in Sect. 3, provides further insights into these issues.

Argumentative Context and Data
We used argument schemes to make an empirical study of what we call "arguments for classification by precent." Our findings illuminate some conceptual questions raised above. In this section, we describe the argumentative context of American civil litigation in which our study arose. We describe our data, methods, and findings only briefly here, but we provide much more detail in the "online supplement" to this article (Larson & Morrison 2023).

American Civil Litigation and Copyright Fair Use
American courts follow the adversarial common-law tradition of the UK. In an American civil case, 12 there are numerous points where the parties ask the court for some relief (e.g. compelling disclosure of evidence, dismissing the suit, etc.), usually by making a motion. The judge's order disposing of the issue may accompany an "opinion" that explains her decision. These opinions have precedential value because other judges can cite them to support the decisions that they make. Copyright fair use is an area of law where they do so.
Normally, a copyright "rights holder" has exclusive rights to copy and make derivative works (adaptations, translations, etc.) of protected works (Larson 2021, p. 159). A "secondary user" or copier of the work is liable for violating a rights holder's exclusive rights. Fair use provides a defense, making a secondary user's otherwise infringing conduct non-infringing where free speech and other public interests are at stake. The legal test for fair use is set out in a statute: The court must determine whether each of four factors weighs in favor of or against fair use and balance them (Limitations on Exclusive Rights: Fair Use 1976). These are fact-intensive inquiries, and courts thus turn to precedent cases to make the fair-use classification. These arguments were the focus of the original data collection for this study and reports of the findings of other segments of it (Larson 2021;. 13

"Legal Analogy" or Classification by Precedent
Proponents of legal arguments in the U.S. frequently use what has sometimes been called "legal analogy," "the effort of lawyers and judges to classify or evaluate operative facts in an instant case, with reference to [facts in] cited cases, to determine whether a particular legal consequence should apply" (Larson 2019, p. 670). 14 This form of exemplary reasoning in American law is most often used to resolve "'problems of classification, where one considers whether a situation comes within the meaning of a rule, [and] 'problems of evaluation,' where one attempts to apply a legal standard like fair use in copyright" (Larson 2019, p. 672 quoting MacCormick 2005. A central issue in normative debates about exemplary arguments in American law is the "covering rule" (Weinreb 2016, p. 61), a rule, at least defeasibly universalizable (MacCormick 2005), that covers the instant and cited cases. According to a frequently cited account, the argument's proponent must abduce a covering rule from a cited case and then apply it to the instant case (Brewer 1996(Brewer , 2018Posner 1990;Schauer 1987 Brewer (1996) embraces this model. Some textbooks teaching legal writing also urge this approach (e.g., Coughlin et al. 2018;Robbins et al. 2019;Shapo et al. 2018;Shultz & Tamer 2020). 17 Larson (2019) proposed an argument scheme without such a covering rule, based in part on work of others (Walton et al. 2008;Weinreb 2016), and argued for its normative status: Here, the proponent does not assert that a universal rule makes the presence of f 1 ... f n a sufficient condition for applying legal category A, but relies on a direct factual comparison between the cases. There are textbooks relating to legal reasoning and writing that urge the construction of arguments in this manner as well (e.g. Chew & Pryal, 2016;Edwards, 2015;Neuman, Jr. et al., 2015, 2017Romantz & Vinson, 2009). 19 We have dubbed exemplary arguments without covering rules "unruly analogies." Proponents can make exemplary arguments with or without covering rules, but previous studies have not empirically examined these arguments to determine how lawyers perform them and other lawyers and judges receive them. The present study sought to extend the work in Larson (2019) to address the empirical and practically normative status of unruly analogies in this context. This forced us to reconsider previous versions of the associated argument scheme, and indeed, the very nature and function of the argument scheme, as noted above.

Data and Analysis
To our knowledge, no study before Larson (2021) had empirically examined the norms of arguments by example in US legal texts. Beginning in 2019, the first author headed a study to characterize the types of uses that lawyers and judges make of previous courts' opinions that they cited in their arguments, reporting the principal findings in Larson (2021). That study examined 199 artifacts, consisting of portions of 55 court opinions and 144 of the parties' briefs that led to them. 20 Each opinion was the core of a "case file" relating to an "instant case," resolving motions by the parties relating to copyright fair use.
The coded spans of the artifacts were segmented and "case uses" identified in each segment: "A case use is a correspondence between one segment of an artifact's argument and a single cited case and encodes the argumentative purpose(s) of citing 18 For an example of this type of argument, see the online supplement (Larson & Morrison 2023) Sect. 2.3. 19 Though not all texts' approaches fell neatly into either of these two camps (see e.g. Clary & Lysaght, 2010;Sinsheimer et al., 2014), the factual and covering-rule approaches were predominant in ten textbooks that we examined. The online supplement (Larson & Morrison 2023) provides examples of other ways that unruly analogies can be constructed, including in citation parentheticals and footnotes in texts. 20 Details regarding data collection and coding, and the data artifacts themselves, are available in an online repository (Larson 2020). Because this study and the supplements to it described in this article used only publicly available documents and did not elicit responses from human study participants, it was exempt from regulation under 45 C.F.R. § 46.104(d)(4) (providing "consent is not required" if applicable "identifiable private information... [is] publicly available") and did not require IRB review. that case in support of the argument in that section" (Larson 2021, p. 165). This was the study's unit of analysis. A pilot study revealed that these authors use cited cases in five principal ways, four to make what Larson described as "rational appeals" and one that functioned both as a rational appeal and a "tactical appeal." 21 These are the four rational appeals (p. 166) 22 : 1. Rule: To "assert the existence of a legal rule before applying that rule to the instant case." 2. Generalization: To "assert that courts in previous cases have generally taken a particular approach." 3. Example: To "describe a previous case, including facts about it and its outcome, to permit the author then to argue that the instant case should come out the same (opposite) way because the cases were (dis)similar." 4. Policy: To "assert that a policy goal or consideration supports a particular outcome." After coding all the artifacts in the study, Larson (2021) reported the relative frequency of uses of the various kinds of case uses.
For each example case use, the presence of the following four characteristics of the case use was noted: 1. Precedent facts. The author drew attention to facts about the cited case. 2. Instant facts. The author drew attention to facts about the instant case that bear some relation to the cited case. 3. Relevant (dis)similarity. The author claimed in this argument section that the identified precedent facts, instant facts, or both, are relevant to this section of the legal argument. 4. Precedent outcome. The author asserted the outcome of the cited case on this legal issue.
These characteristics correspond to the premises in the argument scheme for "legal analogies" proposed in Larson (2019) and discussed above. This article extends Larson (2021). Quantitatively, we tallied argumentation segments in that study, examining the co-occurrence of example and rule case uses at two levels. This study also supplemented the Larson (2021) data by collecting additional briefs from the records relating to each case to assess what judges and advocates consider to be practically normative uses of exemplary arguments. 21 A "'rational appeal'... contributes to the cogency of the argument of which it is a part," while tactical appeals are "argumentative moves... make the argument more persuasive," "adapted loosely from the argumentation-theoretic concept of strategic maneuvering" (Larson 2021, pp. 143-144). 22 The fifth typical case use was to support a quotation from the cited text, something required by American citation standards (The Bluebook: A Uniform System of Citation (2020). The Harvard Law Review Association) but used in both rational and tactical ways in the data. (Larson 2021) described a small number of other types of case use identified in the data for that study. With very few exceptions, however, this article will not deal further with categories of case use other than rule and example.
Qualitatively, we focused on 45 argument segments where at least two cases were used as examples and no case (neither the example case nor any other) was used as a rule. These are paradigmatic unruly analogies. 23 For each case use, we assessed the behavior of three parties: the moving advocate making the exemplary argument, the opposing advocate responding to it, and the judges deciding the case.
Through a close reading of the case use and each document potentially responding to it, we tracked how practitioners and judges made and responded to these arguments through four major categories of data: First, we examined the form of the argument and skeptics' responses for each coding unit, including the depth with which they discussed it. Second, we looked for evidence of covering rules in spite of the original coding in Larson (2021). We reasoned that even where two previous coders had agreed there was no rule to code, some portion of the argument might still be read as a rule. 24 Third, we assessed how the opposing advocate and judge responded to a moving advocate's "unruly analogy." If unruly analogies are not practically normative, we would expect opposing counsel or judges to address the issue. Fourth and finally, we tracked whether opposing advocates and judges based their responses to a moving advocate's exemplary argument on the critical questions proposed by Larson (2019) and revised by Larson (2022). 25 We now instantiate the definition of "argument scheme" we provided in Sect. 2.2 with a new argument scheme for classification by precedent, replacing the argument scheme for legal analogy above. Section 4 presents the new scheme and discusses some implications of this effort.

The Argument for Classification by Precedent
In Sect. 2.2, we proposed a definition of "argument scheme" based in part on the data we have studied in this argumentative context. We instantiate the definition in Sect. 4.1 and discuss it in the context of our empirical findings in the following sections.

Scheme for Argument for Classification by Precedent (AS CbP )
Argumentative context (AC CbP ): This scheme describes arguments for classification by precedent in the context of American civil litigation where the argument's proponent urges application of a legal classification in an instant case, such as "The secondary use is a fair use," based in part on the similarity the instant case bears to a cited court opinion.

Premise-Conclusion Structure (PCS CbP )
Premises (Prem CbP ) Premise 1: Legal category A applied to cited case. 23 We discuss our motivations and methods in the online supplement (Larson & Morrison 2023 With these pieces in place, we can now further discuss some of the theoretical questions above and implications of our empirical findings.

No Relevant Similarity in Prem CbP
Our data supported a change in the premises that appear in Prem CbP from those in the earlier scheme for argument by legal analogy offered above (Larson 2019), which included a premise for relevant similarity. Such a premise had always seemed to us essential for the rational acceptability of an argument of this kind, and it appeared also in Walton et al.'s (2008) Argument from Analogy: Version 2 scheme. In our data, however, it was notably absent, suggesting it does not belong 26 This proposition could spawn a subsidiary argument if some legal authority has defined f x in a way that might include or exclude more instances. For example, perhaps a court previously concluded that operating a skateboard in a park is an instance of operating a "vehicle" in a park. If so, a case involving a skateboard might by definition involve a "vehicle." In a sense then, this proposition responds to Becker's (2016, p. 28) call both to "check the premises" and to "clarify vague expressions." Note that the qualification that most of the features may be present acknowledges that some of the members of Prop may express a degree. 27 These could be differences in facts or in the law that was applied. 28 See the discussion in Sect. 4.4 about the relevance of binding and non-binding precedents.
in Prem CbP . Among the 5638 case uses coded in Larson (2021), 2146 were coded as example, and we examined whether these case uses exhibited the four premise characteristics predicted by Larson's (2019) argument scheme: 1,965 (92%) included facts from the cited case, 1,809 (84%) facts from the instant case, and 1,921 (90%) the outcome of the cited case. In fact, fully 1662 (77%) of the example case uses included all three of these elements, and 1946 (91%) exhibited at least two of them. 29 Of the balance of example case uses, only 141 (7%) included only one of the PCS elements and 59 (3%) included none. 30 These values support the presence in Prem CbP of the Larson (2019Larson ( , 2021 premises other than relevant similarity. In all, only 245 (11%) of these case uses arguably made an assertion or argument about the relevance of those facts. We reviewed the notes coders added to coding units that they identified as having "relevant similarity," finding that, in most cases, they interpreted almost anything that could remotely be considered an assertion about the relevance of the similarity and marked it with this code. Though this is consistent with the coding instructions they received, based on our qualitative review, we were unable to find an example where the argument's proponent truly offered a rationale for the choice of facts. As we shall see, advocates and judges responding to these arguments generally did not raise this issue either, preferring instead to identify relevant dissimilarities.
As we noted above, whether a given set of sentence forms is an instantiation of PCS is largely a descriptive issue: The question is what is typical or conventional within AC. It may sometimes be necessary to regard an instantiation of PCS as an enthymeme and reconstruct one or more sentences representing instantiations of the forms in Prem. But if a such a reconstruction is frequently necessary regarding a particular candidate member of Prem, adding it reduces Prem's descriptiveness. It is an open question how frequently a sentential form should be present in premises actually used to be included in Prem. In this instance however, the nearly complete absence of the relevant-similarity premise in this relatively large sample supports the conclusion that the premise does not belong in Prem CbP with the other premises that were so comparatively frequent.

All members of Prop CbP were Present in the Data
We studied opposing counsel's responses to instantiations of PCS CbP in a subset of our data. 31 Even in this small data set, we observed contradictories of each of the 29 Further work is necessary to explore the extent to which examples without all three premises can be interpreted enthymematically. 30  propositions in Prop CbP , 32 though with varying relative frequencies. The most common strategy (44% of instances) was to assert the contradictory of the No Relevant Dissimilarity proposition, identifying instead a relevant dissimilarity between the cited and instant cases to justify a decision not to apply category A. In the second most common category (22% of instances), the opponent asserted that the argument scheme was not applicable, contradicting the Acceptable Scheme proposition. This included instances where the argument's proponent had asserted a rule governing the cited and instant case, and the opponent denied that the rule was applicable. The third most common approach (14% of instances) was to contradict the Precedent Outcome proposition, in other words, arguing that the argument's proponent was wrong about the outcome of the cited case on the point in question; in effect, contradicting Premise 1 in Prem CbP . Each of the other members of Prop CbP appear in fewer than 10% of the instances. Judges responding to these arguments, however, used only a proper subset of Prop CbP . They used the Relevant Dissimilarity proposition (56%), Similarity proposition (20%), Precedent Outcome proposition (16%), and the Acceptable Scheme proposition (8%) but none of the others. All but the Similarity proposition were also common in opponents' responses. Contradicting the Similarity proposition means contradicting Premise 2 or Premise 3 in Prem CbP .
We take our findings from Sect. 4.2 and this one to support our claim that AS CbP meets Shecaira's standard of minimal descriptive adequacy.

Only Practically Normative
As we noted above, our argument scheme is not normative in any universal sense. For example, AS CbP works in AC CbP , the context of construction, delivery, discussion, and evaluation of a certain kind of legal argument. In theory, propositions in Prop CbP about the relevance of f 1 ... f n would receive support if the judge who wrote the cited opinion said that f x was relevant to their decision and why. Sometimes, judges do express such rationales in their opinions; often they do not. But could one in theory contact the judge of the cited case and ask them? A proposition such as "The judge in the cited case said in an email that f x was relevant to their decision to assign legal category A" could, according to general standards of what is rational, make the argument more cogent. In the argumentative context AC CbP , however, contacting a previous judge like this would be a breach of protocol, and the other parties and judge in the instant case would not consider the information derived from such a contact relevant to the instant case. In short, this proposition would be impermissible in AC CbP .
The Quality of the Cited Case proposition points in the other direction. Among legal theorists in the common-law tradition, it is understood that stare decisis 1 3 operates only when the cited case was wrongly decided: If it were correctly decided, the instant case could be decided using the same principles (Alexander 1996;Bix 2019). In the American context, a judge is free to ignore a badly decided precedent case, but only if the precedent is not a binding one. 33 It is not rational in any universal sense to limit application of the Quality of the Cited Case proposition to nonbinding precedents, but in AC CbP , it is conventionally the case that binding bad decisions are nevertheless binding. 34 These failures to meet a universal normative standard are not a flaw in our proposed argument schemes, because the schemes describe both the argumentative performances and the critical assessment of them that happens within the argumentative context. In this way, we can characterize the practices of legal reasoners empirically. This does not prevent argumentation and legal theorists on the outside from criticizing the CF that lawyers and judges employ in an AC. Consequently, AC CbP is fairly narrowly described here, within the "context of American civil litigation where the argument's proponent urges application of a legal classification." This is due in part to the scope of the data we examined. There are many kinds of arguments and decisions that occur in civil courts-such as determinations of fact based upon evidence-and outside the civil context-in criminal or family law, for example-that may not be amenable to AS CbP .

No Shifted Burdens?
Given the frequent references in the literature to the principle that properly instantiating the premise-and-conclusion structure of an argument scheme shifts some kind of conventional or argumentative burden to the respondent who accepts the premises (e.g. Blair 2012; Godden & Walton 2007a, b;Hansen 2020), our model might be criticized for making no overt reference to this feature of AS. The reason is simple: Our data suggest that an instantiation of PCS CbP does not shift any burden to the skeptics of the argument to respond. In response to the 155 instances of "unruly analogies" we studied in arguments of lawyers supporting their motions for decisions from courts, the opposing counsel ignored them 59% of the time. Judges were even more uninterested in the cases the moving party cited: ignoring them 70% of the time. 35 We believe there are at least two likely reasons for this. First, the 33 Most opinions are not "binding" on other courts. In simplified terms, there are three levels of American federal courts: the U.S. Supreme Court, the court of last resort for all matters; 13 courts of appeal, 12 of which have geographical jurisdictions; and 94 trial courts, called "district courts," at least one in each state or territory and each subject to one of the 12 geographical courts of appeal. For a fuller description, see Administrative Office of the U.S. Courts (n.d.). The American ideal of stare decisis is that appellate courts will respect their own precedents and that all courts will respect those binding precedents of courts superior to them in the court hierarchy. For each district court, binding authorities are the precedents of its own court of appeals and the Supreme Court, but not those of other courts. Despite some risks associated with doing so (see Gardner 2020), courts commonly cite non-binding district-court opinions (Larson 2022 Premise 2(3): The defendant in cited case (and in the instant case) was wearing a baseball cap and interacted with the plaintiff on a Tuesday afternoon.
One could certainly accept and believe the propositions represented in the premises here without adhering to the conclusion. While it is conceivable that these features could represent legally relevant similarities between the two cases, no reasonable person would feel compelled to respond to this argument without more. Second, this rational shortfall may arise because of pragmatic constraints: Opposing counsel are usually subject to page and word-count limits, and judges-especially trial-court judges-are subject to resource constraints, as well, with large caseloads and limited time to respond to all the arguments in all the cases.
That raises the question of when conventional or argumentative burdens can be shifted. We suspect the answer depends on the extent to which the argument's proponent utters sentences representing most or all the propositions in Prop. For example, if we imagine an argumentative context, AC D , where deduction is the principal tool of inference, we might conclude that if one believes the propositions represented in Prem D , one has the burden of accepting/believing C D ; it would be an indefeasible or irrebuttable presumption in a sense because the only propositions in Prop D would be the ones the premises represent.
At the practical level, nothing prevents an argument's proponent in AS CbP from representing other propositions in Prop CbP as premise utterances in an argument. In fact, any lawyer constructing an argument of classification from precedent would be wise to anticipate a skeptic's response, saturating, to the extent possible, the propositions in Prop CbP so that the resulting argument is as strong as possible. Whether they choose to represent those propositions with utterances in the argument is a rhetorical judgment. Were the proponent to fully saturate the argument with utterances representing many or all the members of Prop CbP , an interlocutor who accepted the truth of those premises but not C CbP would probably be regarded as "somehow being illogical or unreasonable..." (Walton et al. 2008, p. 36). Such a saturation of premises suggests that the cited case is "on all fours" with the instant case, "nearly identical in all material ways" to it (Garner, 2019). And such an argument should probably prompt a robust counterargument from opposing counsel and engagement from the judge. On the other hand, countervailing rhetorical or pragmatic reasons may prevent the argument's proponent from generating all the utterances that could represent the contents of Prop CbP .
There could in fact be an intermediate form between the minimal PCS and the maximal representation of all the propositions in Prop that functions as a tipping point for shifting a conventional burden. This seems to us an empirical question: Further research should show whether instantiations of Prem CbP supplemented with utterances representing other members of Prop CbP are more likely to engage 1 3 opposing counsel and judges. Further research in other domains (other ACs) should also show whether instantiations of some PCSs are sufficient in themselves to shift a burden.

Thoughts About the Dialogical Nature of Argument Schemes
Some might object that we do not account for the dialogic nature of argument schemes as posited by key theorists (e.g., Walton et al. 2008;Walton & Gordon 2011;contrast Lumer 2022). Despite the necessarily social origins of PCS and CF, we do not claim that an argument scheme itself is necessarily dialogic. A single person can instantiate CF to determine the strength of a possible argument based on the scheme. Having done so, it is up to them whether to utter sentences based on PCS.
Whether the members of Prop should be instantiated as questions or propositions depends on the AC. It is appropriate that we have framed Prop CbP not as questions but as statements, because opposing counsel and judges in our study uttered sentences the pragmatic effect of which was to contradict propositions in Prop CbP . Of course, for an argument skeptic engaged in an actual dialogical situation with the argument's proponent, the skeptic may convert all propositional forms in any Prop to questions according to the practice of Walton et al. (2008) and others. An argument's audience could use critical questions to instantiate a critical framework, but they did not do so here in AS CbP .
In any event, it is not clear whether the arguments in our study are dialogical. Shecaira (2016, p. 515) doubts that arguments in formal legal contexts are in fact dialogical, because the judge is not subject to critical questioning in the same way parties are. Nevertheless, in our view the judge adopts an opinion with knowledge that it may generate a response from the parties because "Legal arguments... always anticipate a response" Larson (2022, p. 753). The pattern we observed in our data was more like the "three-ply" process involving moving and opposing lawyers that Atkinson and Bench-Capon (2021, p. 420) describe: "(1) The proponent presents an argument (2) The opponent responds to the argument (3) The proponent attempts to rebut the response." We would add a move from the judge at the end. We therefore adopt the perspective that the instantiation by a party of PCS CbP is qualifiedly dialogic. Our definition is adaptable to argumentative contexts and argument schemes that are fully dialogic or fully monologic, but further research will determine whether they exist.

Conclusion
Our definition of "argument scheme" and our data regarding instances of the argument scheme for classification by precedent in American judicial texts work together to offer ways through certain challenges to argument-scheme theory. Our solution depends on the concept of the argumentative context and its governance of the premises and conclusions of an argument scheme and the critical framework for it. We showed how viewing the premise-and-conclusion structure of an argument scheme as descriptive can allow the researcher or analyst to decide which sentence forms are part of the premises and conclusions and which are not. We also articulated a standard for determining whether the critical framework includes all the propositions (or critical questions) that are relevant to the scheme for audiences in the argumentative context, another empirical question. We have acknowledged, however, that any normativity in the argument scheme is only practical, not rationally universal. The argumentation theorist or legal philosopher could certainly challenge the practices of lawyers and judges, even their practically normative assessments, on normative-or as we said, "meta-normative"-grounds.
We do not believe the argument scheme we have developed here imposes any conventional or argumentative burdens on its recipients; nevertheless, we have suggested means by which an argument's proponent could use the critical framework of our scheme to attempt to shift that burden. Finally, though an argument scheme may be suited to dialogical contexts, we do not assume that they have a dialogic nature.
Much further research is necessary to assess our approach to argument schemes. For example, we have not delivered an answer to the question that motivated our study: Whether unruly analogies are practically normative in this argumentative context. Our data showed no instance of an opposing attorney or judge complaining about the form of an advocate's argument based on it lacking a covering rule, but our research also showed that opposing counsel and judges simply ignored many such arguments. To answer our motivating question, we will have to compare the treatment of unruly analogies to exemplary arguments with covering rules and to other widely accepted legalargument types to see whether opposing counsel and judges reacted differently to them. We might also seek to see whether the appearance of unruly analogies correlates with parties' success or failure in their motions.
Our findings regarding the members of Prop CbP are also potentially much hampered by the small size of our data set. In statistical terms, our study has little power, meaning that a bigger set of data might have yielded evidence of other types of challenge to arguments proposed using PCS CbP , that is, other members of Prop CbP . Further, more-focused study in our own data is also necessary to discover whether other proposition forms that belong in Prop CbP might have escaped our attention, guided as we were by earlier work of the first author. More study is also necessary to understand why opposing advocates and judges chose the members of Prop CbP that they used and what they take the pragmatic effect of their use to be. It would also be interesting to see how the members of Prop CbP categorize under, and whether they meet the requirements of, the frameworks of Lumer (2022) and Yu and Zenker (2020). Finally, we relied on our training, anecdotal experiences, and intuitions to conjecture that AC CbP accurately describes those contexts where AS CbP is acceptable, even though our data related only to copyright fair-use matters. This, too, is an empirical question that deserves further research. Analogous empirical questions would arise, of course, in the study of other schemes and other argumentative contexts.
Meanwhile, the work of this article has allowed us to structure our thinking about argument schemes in a manner that facilitates our work and hopefully the work of other researchers.