A Generalizable Argument Structure Using Defeasible Class-Inclusion Transitivity for Evaluating Evidentiary PDF

A Generalizable Argument Structure Using Defeasible Class-inclusion Transitivity for Evaluating Evidentiary Probative Relevancy in Litigation JOSEPH A. LARONGE, Oregon Department of Justice, Salem, OR, USA; 1162 Court Street N.E. Salem, OR 97301, USA. E-mail: [email protected]...

A Generalizable Argument Structure Using Defeasible Class-inclusion Transitivity for Evaluating Evidentiary Probative Relevancy in Litigation JOSEPH A. LARONGE, Oregon Department of Justice, Salem, OR, USA; 1162 Court Street N.E. Salem, OR 97301, USA. E-mail: [email protected] Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 Abstract A new argument structure based on defeasible class-inclusion transitivity (DCIT) is proposed as a generalizable structure for evaluating probative relevancy determinations in litigation across typical evidentiary fact patterns. The general applicability for deductive inferences can be seen through the use of Sommers term-functor logic (TFL) principles to regiment premises into a DCIT structure. Its generalizability for inductive and presumptive (e.g. plausibilistic) inferences can be demonstrated by translating a variety of informal logic structures (e.g. Toulmin, argument schemes, Wigmorean charts and conventional box and arrow diagrams) into a DCIT argument structure. A proper use of a DCIT structure demonstrates whether the item of evidence offered to be admitted in the trial and the ultimate probandum of the case (e.g. the defendant is guilty of murder) are linked within a single structurally correct argument. A DCIT perspective also provides a coherent metaphorical explanation of the concepts of probative force, probative weight, linked and convergent premises and inference. Keywords: Probative relevancy, defeasible class-inclusion transitivity, argument mapping, universal logic, term-functor logic. In a federal trial in the USA, an item of evidence must have probative relevancy, as determined by the court, to meet one of the requirements for admissibility into evidence in the trial. The applicable legal standard is whether the evidence has ‘any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence’. Federal Rules of Evidence (FRE) 401. The Notes of the Advisory Committee on Rules to FRE 401 further explain this test: Relevancy is not an inherent characteristic of any item of evidence but exists only as a relation between an item of evidence and a matter properly provable in the case. Does the item of evidence tend to prove the matter sought to be proved? Whether the relationship exists depends upon principles evolved by experience or science, applied logically to the situation at hand. ***** The fact to be proved may be ultimate, intermediate, or evidentiary; it matters not, so long as it is of consequence in the determination of the action. (Notes, FRE 401) Since the ‘fact to be proved’ must be ‘of consequence to the determination of the action’, if it is not the ‘ultimate’ fact at issue (e.g. whether the defendant is guilty of murder), then the ‘fact to be proved’ must at least have probative relevancy to the ultimate fact (i.e. ultimate probandum) to be of consequence. And since relevancy in this context must be transitive , the item of evidence for which admission is sought must also have probative relevancy to the ultimate probandum (Figure 1). Vol. 22 No. 1, © The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected] Published online 2 December 2009 doi:10.1093/logcom/exp066 130 A Generalizable Argument Structure item of fact that is of ultimate evidence consequence probandum probative relevancy probative from transitive relation relevancy Figure 1. FRE 401 probative relevancy through transitivity. This transitive relevancy connection is reflected in the merging of two traditional concepts in the FRE 401 definition of relevance. The connection between the item of evidence and the fact to be Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 proved, prior to the enactment of FRE 401, was also called relevance. And the connection between the fact to be proved and the ultimate probandum was called materiality. These two concepts were combined under the new definition of relevance in FRE 401 (State v. Guzek, 2007). Proving or refuting this logical connection to the court, however, can be a significant challenge for a litigator. This article proposes a new generalizable argument structure to make overcoming this challenge easier. To show ‘the relationship... applied logically’ (Notes, FRE 401) between the item of evidence offered to be admitted and the ultimate probandum, both must be shown to be contained within a single structurally correct argument which the court accepts. Structural correctness does not require that the argument is necessarily deductively valid or inductively strong. In this context, structural correctness means that the design or form of both the argument and the individual premise structure permit probative weight (e.g. acceptability), if any, to reach the ultimate probandum, thereby, making it more or less probable. Given that this court determination is often made within a few minutes in open court, being able to quickly prove or refute this structural correctness to the court is critical. Oddly, however, while argumentation is fundamental to the practice of litigation, attorneys and judges, as law students, are not typically trained in a rigourous application of formal or even informal logic. A comprehensive training in the science of proof has been largely neglected in legal education.1 And as Woods [34, p. 2] points out, ‘there remains a lot of resistance by lawyers and legal scholars to the analytical and methodological norms championed by logicians’. Under these conditions, presenting a rigourous analysis to the court about claims of probative relevancy can be difficult. Further, since probative relevancy in litigation often depends upon an inference-upon-inference chain of reasoning (e.g. multi-leveled argument), with a combination of multiple modes of inference, some of which may be defeasible , minimizing unnecessary complexity in the argument structure is important for a prompt and correct determination of the structural correctness of the argument by the court. The exploration for a suitable argument structure to meet this challenge begins with an examination of methods used to determine validity for deductive inferences that occur in litigation. Using modern predicate logic (MPL) to demonstrate structural correctness to the court is considered first. It is not an appropriate choice for a number of reasons. It relies upon many logical forms. And it needs many vehicles to show such forms. Thus, it is far removed from the familiar natural language used by the court. Finally, MPL is not typically part of a shared logical understanding between the attorney and the court. 1 In recent years, there have been some law schools that offer science of proof law courses. Anderson et al. is a commonly used textbook for these courses.  A Generalizable Argument Structure 131 As an alternative, Sommers term-functor logic (TFL) is a big step in the right direction for effectively demonstrating probative relevancy in deductive arguments. It overcomes the weaknesses of traditional term logic, while retaining the familiarity of categorical reasoning. The syntax is natural. It is as powerful in application as MPL and, yet, less complex. Further, it is psychologically realistic. And it has relatively simple decision procedures for validity. But, despite its comparative simplicity, solving unfamiliar semantic algebraic equations, as TFL requires, will not function for the uninitiated in a courtroom. The author proposes, however, that the customary articulated forms in TFL can be used to algebraically transform an argument into a single familiar argument structure that makes structural correctness readily apparent for purposes of probative relevancy determinations involving deductive, as well as, inductive and presumptive (e.g. plausibilistic) modes of inference. The generalizable argument structure proposed relies upon a single mode of inference, namely, class-inclusion transitivity (CIT) [12, p. 88]. As Groarke analogizes to the parable of the fox and Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 the hedgehog, a single mode of inference that always works, like the hedgehog’s single trick, has advantages over the 36 inference tricks of the fox. And unlike a structure that chains together multiple inference types (e.g. deductive, inductive and presumptive), some of which may be unfamiliar to the court, comprehending an inference using CIT is a customary step in child development. This means that the attorney and the judge will have a shared understanding of how this mode of inference functions. As part of a fundamental cognitive developmental stage, it may also lend some support that CIT reflects to some degree how humans may more universally reason. If this connection is accurate to some degree, CIT would be cognitively veridical (i.e. describing how people actually reason) as the concept is described in Sommers , likely making it easier for the court to quickly comprehend it. As an additional advantage, a CIT argument structure brackets the item of evidence under consideration between the subject phrase and predicate phrase of the ultimate probandum. The subject phrase of the ultimate probandum sentence is the start and the predicate phrase of the ultimate probandum is the finish of this inference bridge. Therefore, the placement of the item of evidence at issue in the argument structure can, perhaps, be more easily oriented in the structure by being located between two constant points, rather than targeting a single point (i.e. ultimate probandum) as is done with customary argument extrapolation to show probative relevance. And since CIT can be analogized, as depicted in subsequent figures, to the judge physically moving along a path of dots to reach the ultimate probandum, this argument structure may tap into an embodied understanding of the nature of reasoning [15, 26] that may also help increase its comprehension by the court. There are strong clues that CIT can serve as a generalizable form for evidentiary issues that require a customary formal logic deductive approach to reveal structural correctness (e.g. well-formedness). As Englebretsen [7, p. 63] points out, ‘it has been argued off and on for centuries that the fundamental rule governing syllogistic inference is dictum de omni—the rule of all’. And Sommers and Englebretsen [21, p. 141] show how dictum de omni (DDO) can be applied as well to relational arguments, all of which can be constructed as relational syllogisms. The CIT connection is that its underlying rule is DDO, namely, ‘whatever is true of all M is true of whatever “M” is true of … Another, more general, way of the thinking of the dictum is as a rule of substitution’ [7, p. 63]. It can be written as ‘DDO: E(M), E*(-M)/E(E*)’ [21, p. 141]. This same formula can be extended into a longer chain of inference using CIT. The proposed argument structure, except for an additional feature that accounts for defeasibility to be discussed later, is related to the TFL transitive chain presented by Sommers and Engelbretsen [21, p. 125] as follows: ‘+[−A+ B] + [−B + C] + [−C + D] + [−D + E]’ where A is the subject phrase term of the first premise and E is the predicate phrase term of the last premise in the 132 A Generalizable Argument Structure chain which together algebraically equal the main conclusion. The precise CIT algebraic expression for this proposed argument structure is as follows: (A/B) (B/C) (C/D) (D/E) = A/E. The numerator position is for the complex subject phrase and the denominator position is for the complex predicate phrase of each premise. Through the operation of multiplication, the middle complex phrases are canceled. This new CIT algebraic identities formulation does not use the positive and negative signs of TFL. Proof of syllogistic validity in TFL has two requirements. First, the syllogism must be either U-regular or P-regular [21, p. 109]. This means that either the syllogism contains only universal statements (i.e. U-regular) or the syllogism contains precisely two particular statements one of which is the conclusion (i.e. P-regular) [21, p. 109]. Second, the premises, as represented algebraically, must add up to the conclusion [21, p. 110]. Significantly, these two requirements define the basic argument structure of CIT [21, p. 125]. The first premise in a CIT chain is either universal or particular. If it is universal, all the remaining premises and the conclusion are universal. If the first premise is Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 particular, then the only remaining statement that is particular is the conclusion. And through the correct canceling of the middle terms, which may be complex terms, the product resulting from the multiplication of the premises always equals the conclusion. To apply a CIT template to an argument, regimentation of the natural language terms is performed where necessary, with processes such as obversion, passive transformation [21, p. 97], reordering conjuncts [21, p. 97] and laws of identity [21, p. 131], to conform the premises to this transitive canonical form and order. Sommers and Englebretsen [21, p. 149] provides an example of the basic process of transforming arguments. To complete the transformation for CIT, implicit premises are added to the structure as necessary with an enthymematic argument. As a result, a CIT argument structure enables the litigator to scaffold all structurally correct arguments so that these two requirements are apparent. Alternately, if the argument cannot be regimented to fit within the CIT argument structure, it is not structurally correct. Conceptually then, CIT can be envisioned with a set-theoretic perspective of predication with the complete subject phrase and the predicate phrases being classes. While predication is more than class-inclusion or membership [4, p. 123], a class-inclusion perspective functions pragmatically. Logical reasoning can then be reduced to the act of providing a series of phrase predicates that act as nested class linkages that demonstrate that the subject phrase of the main conclusion is included in the class of the predicate phrase of the main conclusion at the outer dimensions of the nesting. In effect, the main conclusion is unzipped and some of the implied phrase predicates are unpacked. CIT should not be conflated with the transitivity of predication. ‘[F]or all we affirm of the predicate will also be affirmed of the subject’. Angelelli notes that this statement is restricted to essential predication, which occurs when the predication is as of a subject. To illustrate, consider the following example: Premises: The Braeburn apple is red. Red is a colour. Conclusion: So the Braeburn apple is a colour. The transitivity of predication is not applicable in this argument. This is because ‘red’ is not essentially predicated of ‘the Braeburn apple’. This example is not, however, representative of a CIT argument structure. Rather, using CIT the first premise would be stated as ‘The Braeburn apple is included in the class of “is red” ’. From this perspective, it is clear that the previous argument structure is incorrect. To be structurally correct, the second premise would be stated as ‘Any that is red is a colour’. With this argument structure, the transitivity of class-inclusion is applicable and indicates a structurally valid argument even though it is not sound. Similarly, CIT should not be conflated with any transitive relation other than class-inclusion. For example, consider the following argument: A equals B, B equals C, so, A equals C. This is  A Generalizable Argument Structure 133 not a CIT structure either. Rather, as detailed later, the argument would be structured using CIT as follows: A equals B. Any that equals B equals C (with the necessary assumption that B equals C). So, A equals C. The CIT premise structure can be represented with a semantic diagram as follows: Sc—⊙— p1—⊙—p2—⊙—p3—⊙—pn—⊙—pc. The metaphoric symbol —⊙—indicates ‘is included in the class of’. So this transitive chain would be read as ‘The complete subject phrase of the main conclusion is included in the class of the complete predicate phrase number one which is included in the class of the complete predicate phrase two... (etc.) which is included in the class of the complete predicate phrase of the main conclusion’. To enhance its generalizability in a litigation setting, I have added a feature to CIT to account for defeasibility in the proposed argument structure. Conclusions in litigation are, prior to a final court judgement, often subject to alteration by the introduction of new evidence. The addition of a defeasibility component to CIT results in what I have named as defeasible CIT (DCIT). The effect of Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 the addition of defeasibility to CIT is similar to transforming modus ponens into defeasible modus ponens. The CIT algebraic formulation is, thus, changed to a DCIT conditional algebraic equation in which the non-transitive assumptions added for purposes of defeasibility act as conditionals to the DCIT equation. To illustrate DCIT’s versatility and power, first a series of examples adapted directly from will be illustrated. Englebretsen’s examples were used to illustrate the power of TFL with simple terms, relationals, conditionals and others. Some of these TFL examples will also be depicted as Englebretsen line-drawing diagrams. And then a transforming of that TFL example into its fundamental DCIT argument structure will be illustrated with both a textual template and two versions of DCIT diagrammatic forms. The DCIT categorical diagrammatic form illustrated is not to be confused with a Venn diagram. Yet, it does function as a type of proof vehicle for structural correctness. It is a metaphoric representation of nested containers as nested classes consisting of, after the first subject phrase, predicate phrases. It reflects the fact that any English sentence can be depicted as a dyadic structure [21, p. 92], consisting of a subject phrase and a predicate phrase. This dyadic structure is then simply regimented into a DCIT form with the premises algebraically equalling the conclusion and where the distributed middle terms can be cancelled correctly. The black vertical supports in this diagrammatic form reflect the functions of assumptions that are inherent in any particular assertion of class inclusion. They can be thought of as statements about the world under analysis. These supports account for the defeasible nature of inference that is often typical in litigation. For greatest efficacy, they can reflect both adjunct assumptions and necessary assumptions as discussed later. The other DCIT diagrammatic form illustrated is more typical of an argument graph with edges and nodes. But, it also functions metaphorically by representing the argument as a supported inference bridge that can be traversed, leading to the ultimate probandum. Each line-span of the bridge represents the class-inclusion relationship between the subject phrase and predicate phrase of each premise. Beneath each span is a vertical support that represents the adjunct and necessary assumptions for that relationship. This diagram form can be used in a lateral or aerial perspective. The hiking figure represents the judge carrying subjective acceptability, as probative weight. The judge moves towards the ultimate probandum with the amount of acceptability that can be sustained by the probative weight bearing capacity of all the spans. As Englebretsen [7, p. 41] states, ‘all valid syllogisms can be reduced to first figure syllogisms.’ The first-figure syllogisms are illustrated with his linear diagram treatment and then DCIT diagrams will illustrate how they all reduce to a DCIT form with examples adapted directly from Englebretsen [7, p. 41]. 134 A Generalizable Argument Structure BARBARA (Figures 2–5): Every A is B. Every B is C. So every A is C. C B A Figure 2. Englebretsen linear diagram for BARBARA form. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 [There are no Every A relevant assump- tions.] is B [There are no relevant assump- is C tions.] Figure 3. DCIT categorical inference diagram for BARBARA form. Every A is B is C Every A is C [assumptions] is included in the class of... [uni-directional] Figure 4. DCIT inference bridge diagram for BARBARA form. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 Every A......is B. [no relevant assumptions] 2 Any...is B......is C. [no relevant assumptions] who (that) CONCLUSION 3 Every A is C. Figure 5. DCIT inference template for BARBARA form.  A Generalizable Argument Structure 135 In less natural terms, this argument would read as follows: Every A is included in the class of ‘is B’. Any that is included in the class of ‘is B’ is included in the class of ‘is C’. So, every A is included in the class of ‘is C’. Note that the phrase predicate, if it exists, is used as the category. DARII (Figures 6–9): Every A is B. Some C is A. So some C is B. A C B Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 Figure 6. Englebretsen linear diagram for DARII form. [There are no Some C relevant assump- tions.] is A [There are no relevant assump- is B tions.] Figure 7. DCIT categorical inference diagram for DARII form. Some C is A is B Some C is B [assumptions] is included in the class of... [uni-directional] Figure 8. DCIT inference bridge diagram for DARII form. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 Some C......is A. [no relevant assumptions] 2 Any...is A......is B. [no relevant assumptions] who (that) CONCLUSION 3 Some C is B. Figure 9. DCIT inference template for DARII form. 136 A Generalizable Argument Structure Following TFL principles for relationals, ‘syntactically complex terms’ are admitted ‘into the roles traditionally reserved for terms in categoricals’[7, p. 47]. To illustrate, these examples (Figures 10–13) are adapted directly from Englebretsen [7, p. 51]. Some detective gave some money to every Justice. Every Justice is bound by an oath. Every detective is a court official. Every oath is sacrosanct. So some court official gave some money to someone bound by something sacrosanct. D C G M Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 B some Q J B Q S Figure 10. Englebretsen linear diagram for relational 1. Some court official Some detective gave some money to gave some money every Justice to every Justice. gave some money to Every detective is someone bound by a court official. an oath Every Justice is gave some money to bound by an oath. someone bound by something sacro- sanct Every oath is sacrosanct. Figure 11. DCIT categorical inference diagram for relational 1.  A Generalizable Argument Structure 137 [assumptions] is included in the class of... [uni-directional] Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015. Figure 12. DCIT inference bridge diagram for relational 1. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 Some court...gave some Some detective gave some official... money to every money to every Justice. Justice. Every detective is a court official. 2 Any...gave some...gave some Every Justice is bound by an who money to every money to some- oath. (that) Justice... one bound by an oath. 3 Any...gave some...gave some Every oath is sacrosanct. who money to money to some- (that) someone bound one bound by by an oath... something sacrosanct. CONCLUSION 4 Some court official gave some money to someone bound by something sacrosanct. Figure 13. DCIT inference template for relational 1. The following example (Figures 14–18) is directly derived from Englebretsen [7, p. 54]. Aristotle has all the properties of greatness. Wisdom is a property of greatness. So, Aristotle is wise. 138 A Generalizable Argument Structure A H P Aristotle has wisdom. Figure 14. Englebretsen linear diagram for relational 2. H A W Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 Aristotle is wise Figure 15. Englebretsen linear diagram for relational 2. Aristotle [no relevant assumptions] has all the properties of greatness [no relevant assumptions] has wisdom is wise [no relevant assumptions] Figure 16. DCIT categorical inference diagram for relational 2. [assumptions] is included in the class of... [uni-directional] Figure 17. DCIT inference bridge diagram for relational 2.  A Generalizable Argument Structure 139 DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 Aristotle...has all the [no relevant assumptions] properties of greatness. 2 Any...has all the...has wisdom. [no relevant assumptions] who properties of (that) greatness... 3 Any...has wisdom......is wise. [no relevant assumptions] who (that) Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 CONCLUSION 4 Aristotle is wise. Figure 18. DCIT inference template for relational 2. The following example (Figures 19–21) has a minor term relational. It is adapted directly from Englebretsen [7, p. 64]. Note that here a minor relational term requires an assumption which allows a substitution to fit within the DCIT structure. Every A is B. Some/every C is R to some A So some/every is C is R to some B C R B A Figure 19. Englebretsen linear diagram for relational 3. Some/every C is R to some A Every A is B. is R to some B Figure 20. DCIT categorical inference diagram for relational 3. 140 A Generalizable Argument Structure DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 Some/every C...is R to some A. 2 Any...is R to some...is R to some Every A is B. who A... B. (that)... CONCLUSION Some/every C is R to some B. Figure 21. DCIT inference template for relational 3. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 The following example (Figures 22–26) has a relational major term. It is adapted directly from Englebretsen [7, p. 64]. Some/every A is B Every B is R to some/every C So some/every A is R to some/every C. A C A R B Figure 22. Englebretsen linear diagram for relational 4. Some/every A is B [no assumptions] is R to some/every C [no assumptions] Figure 23. DCIT categorical inference diagram for relational 4.  A Generalizable Argument Structure 141 DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 Some/every A...is B [no relevant assumptions] 2 Any...is B...is R to [no relevant assumptions] who some/every C (that)... CONCLUSION Some/every A is R to some/every C. Figure 24. DCIT inference template for relational 4. The following is a similar example (Figure 25) with a modus tollens form after regimenting the Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 premises into a DCIT form. If Bob stays, Jane will leave. Jane is not leaving. So Bob is not staying. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 The state of...is Jane is not affairs leaving. 2 Any...is Jane is not... is Bob is not who leaving.. staying. (that)... CONCLUSION 3 The state of affairs is Bob is not staying. Figure 25. DCIT inference template for modus tollens. The following example (modus ponens) (Figure 26) is adapted directly from Englebretsen [6, p. 58]. If Bob stays, Jane will leave. Bob will stay. So Jane will leave. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 The state of...is Bob will affairs stay. 2 Any...is Bob will... is Jane will who stay... leave. (that) CONCLUSION 3 The state of affairs is Jane will leave. Figure 26. DCIT inference template for modus ponens. 142 A Generalizable Argument Structure An inference-upon-inference tree-like or pyramid argument structure of deductive inferences also reduces, with redundancies removed, to a less complex DCIT structure. For example, Richard Whately, the English Logician and Archbishop of Dublin, created such a structure in what may have been the first use of argument diagramming [29, p. 263]. Figure 27 represents this Whately (1826, p. 422 as cited in Walton [29, p. 263]) structure. Figure 28 illustrates with arrows the CIT inherent in this structure starting at node Z. And Figure 29 represents the same argument with redundancies removed as a DCIT argument structure. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 Figure 27. Richard Whately argument diagram of inference-upon-inference. Figure 28. Richard Whately argument diagram of inference-upon-inference showing inherent class- inclusion transitivity.  A Generalizable Argument Structure 143 Z A Y C B X Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 Z is X is included in [assumptions] the class of... [uni-directional] Figure 29. DCIT inference bridge diagram of Richard Whately inference-upon-inference. This simplification applies regardless of the size or configuration of the argument pyramid [16, 17]. The multiple end points of the pyramid can always be restated by starting with the subject phrase of the ultimate probandum. This feature makes sense since any premise must ultimately connect into the ultimate probandum. The Whately pyramid structure is a natural transition point as informal logic structures are now considered. The reason is that this original Whately argument structure is also common in informal logic contexts. For example, Rationale™ and Araucaria are two argument visualization software programs that rely upon this tree-like or pyramid structure. Like the Whately example, these programs similarly also create unnecessary redundancies by indicating sub-conclusions as the premises are stacked towards the main conclusion at the top. These redundancies can cause problems in the litigation context. First, it increases unnecessarily the length of the inference chain that the court must consider. When time for consideration is at a premium in open court, this added complexity puts an increased demand on the time available. Second, the use of visualizations of the argument structure to increase the comprehension of the court becomes more problematic as the number of premises increases. When an exhibit cannot fit on an 81/2 × 11 inch page for use as an overhead transparency or as a Powerpoint slide, its applicability is reduced in open court. There are two more problematic issues for litigation with the use of these argument structures that rely upon the conventional box and arrow visual grammar. A significant problem is that these approaches do not have a structural requirement for the form of the premises that ensures structural correctness. Any form of a premise can be placed within their boxes (Figure 30). This lack of a clearly defined premise structure means that the logical connection between the item of evidence and the ultimate probandum may not be readily apparent to the court even when the boxes and arrows (i.e. node and link) connect. Or it may not exist at all. Twardy discusses the difficulties that university students experience in filling in these boxes correctly in order to achieve structural correctness. 144 A Generalizable Argument Structure conclusion premise 1 premise 2 Figure 30. Box and arrow argument diagram. Another problem with the box and arrow visual grammar is that it does not easily account for Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 necessary and adjunct assumptions in its argument structure. For example, as will be discussed later regarding Figure 44, inferences drawn from a witnesses’ statement depend on assumptions such as the fact that the witness was able to recall the event correctly. The typical use of the box and arrow visual grammar requires that this assumption be shown as another box in line with the other premises at that level of the argument. This placement makes it difficult to clearly distinguish between premises that are strictly linked and those that connect through providing support as an assumption. The familiar Toulmin informal argument structure also provides an informal logic example. It also lacks a premise form requirement which can result in the linkage being obscured. For example, Figure 31 depicts Toulmin’s well-known argument that Harry is a British subject. CLAIM DATUM WARRANT BACKING Figure 31. Toulmin argument diagram of ‘Harry is a British subject’. Consider a hypothetical fact where the attorney argues that the BACKING (i.e. the British Nationality Act identifies anyone born in Bermuda as a British subject) has probative relevancy to the claim that Harry is a British subject. This argument structure does not make this relevancy readily apparent. Any text could be entered into the BACKING text block within the rigour demanded of this argument structure. To the contrary, the following DCIT template, Figure 32, translates this argument into a DCIT structure that provides the rigour to make this logical linkage obvious. And Figure 33 shows this DCIT argument structure in a diagrammatic form.  A Generalizable Argument Structure 145 DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 Harry...was born in [no relevant assumptions] Bermuda. 2 Any...was born in...is identified by [no relevant assumptions] who Bermuda... the British Na- (that) tionality Act as a British subject. 3 Any...is identified...is a British [no relevant assumptions] who by the British subject. (that) Nationality Act as a British subject... Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 CONCLUSION 4 Harry is a British subject. Figure 32. DCIT inference template of ‘Harry is a British subject’. Harry was born in Bermuda is identified by the Brit- ish Nationality Act as a British subject is a British subject is included in [assumptions] the class of... Harry is a British subject. [uni-directional] Figure 33. DCIT inference bridge diagram of ‘Harry is a British subject’. This example also illustrates that the judge need not be familiar with different classifications of premises (e.g. Toulmin’s datum, warrant and backing), since these differently labelled premises can all be translated into a chain of premises with identical class-inclusion nesting characteristics. Labelling premises becomes, therefore, unnecessary and, perhaps, misleading. At least as to warrants and backing, Hitchcock also suggests that there is no need to propose a clear difference. (Pinto provides an alternate perspective. And Freeman proposes making distinction between warrants based on their purported different epistemic modes.) Further, from this DCIT argument structure 146 A Generalizable Argument Structure perspective, such labelling is revealed to be only provisional until further classes of complete predicates, if any, are placed between them. This provisional nature of Toulmin labels can be illustrated with an example of conditional relevance. ‘With conditional relevance, probative value depends not only upon satisfying the basic requirement of relevancy as described above but also upon the existence of some matter of fact. For example, if evidence of a spoken statement is relied upon to prove notice, probative value is lacking unless the person sought to be charged heard the statement (Notes, FRE 401)’. For example, the court, in the previous Harry argument, hypothetically might state that the item of evidence that ‘Anyone born in Bermuda is identified by the British Nationality Act is a British subject’ is only accepted as conditionally relevant (Notes, FRE 401), dependent on the claim that ‘Harry was born in Bermuda’ being shown to the court to be plausible to some degree. In effect, the court is saying that it needs at least one intervening nested predicate phrase class between ‘Harry’ and ‘was born in Bermuda’. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 To meet this condition hypothetically, the attorney might produce evidence that ‘Harry has a Bermuda birth certificate’ with the addition of the phrase predicate ‘has a Bermuda birth certificate’ shown circled in Figure 34. If the court accepts this claim to some degree and the adjoining claim that ‘One who has a Bermuda birth certificate was born in Bermuda’, the connection between ‘Harry’ and ‘was born in Bermuda’ could be shown to the court as illustrated in Figure 35. Depending on the court’s acceptance of any particular class inclusion relationship within the argument, a differing degree of granulation between the nested predicate phrases may be needed to persuade the court.2 Harry has a Ber- muda birth certificate was born in Bermuda is identified by the British Nationality Act as a British subject is a British subject Harry is a British is included in [assumptions] subject. the class of... [uni-directional] Figure 34. DCIT inference bridge diagram of ‘Harry is a British subject’ unzipped. 2Aristotle, according to Hintikka [12, p. 89], argues that the continuing granulation never reaches infinity. Rather, he argues that it ultimately ends in a definition.  A Generalizable Argument Structure 147 John Henry Wigmore’s chart method is another informal logic argument structure to compare with DCIT. It was developed for legal scholarship. It went over, however, like a ‘lead balloon’ [24, p. 165]. One of its difficulties may have been its complexity. Anderson et al. have attempted to revive its use with suggested modifications. Neither the Wigmore chart method nor their modifications, however, provide a required form for premises that would clearly established a linkage between the premises. And in Wigmore’s examples, many of the connections between the premises relied upon implicit premises. Figure 35 is an example of a charting of evidence done by Wigmore. Here, P Driver S did deliver the money to clerk H; plaintiff denies this, i. e. his Pn Driver S did not deliver it. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 T1 H’s receipt testimonially admitting the delivery P2 S did deliver. This is explained away by C1 H’s practice (testified to by himself T5) to sign the receipt although the goods were left on the sidewalk and not brought to him. T2 H’s testimony on the stand that the package was not delivered. T3 F’s testimony to C2 the company’s rule requiring complete delivery by drivers, and this C2 C3 the habit of drivers in general to deliver com- pletely, which C4 the habit of driver S to deliver com- pletely. But T4 H’s testimony that S did not habitually do so. Then C5 S’s thieving prac- tices (testified to by F T6) P1 he did not deliver the money, but kept it for himself. Thus, the evidence would plot: Thus, if we accept C1 as explaining away T1, and doubt C4 because denied by T4, and if we give credit to T2 and C5, we arrive at the final inference (as the Court did) that the money package was not delivered. Figure 35. John Henry Wigmore chart method diagram of American Express. In this case, American Express Co. v. Haggard, 37 Ill 466 (1865), the issue was whether a package of money was ever received at the David D. Haggard business through delivery by American Express. While there was a signed receipt that the money was delivered to Mr Haggard’s son, a clerk H, at the business, his son claimed that the package was never delivered. Figure 36 illustrates a DCAT argument structure for these inferences which makes the connections between the premises apparent. This example also illustrates the concept on attacking the opponent’s arguments, which is discussed further in the following section. Figures 37–41 show the Wigmore argument in a DCIT template format. 148 A Generalizable Argument Structure Defendant D1 D8 subject phrase P4 P1 D2 D9 interim predicate phrase D3 final predicate P5 phrase Plaintiff P2 D4 is included in P9 is included in the class of... the class of... [uni-directional] P3 P8 [uni-directional] Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 P6 D5 [assumptions] [assumptions] P7 D6 arrow = transitive step arrow = transitive step D7 blocking objection Figure 36. DCIT inference bridge diagram of American Express. DEFENDANT’S 1ST INFERENCE LINE Subject phrase Predicate phrase D1 Driver S...was a driver for Am. Express. D2 Any...was a driver for Am. Ex-...was, according to F’s testimony, who press... subject to the company’s rule for all drivers, requiring complete delivery. D3 Any...was, according to F’s testi-...was subject to the company’s rule, who mony, subject to the com- for all drivers, requiring complete pany’s rule for all drivers, delivery. requiring complete delivery... D4 Any...was subject to the com-...was in a class of drivers which in who pany’s rule, for all drivers, general had the habit for complete requiring complete delivery... delivery. D5 Any...was in a class of drivers...had the habit to deliver completely. who which in general had the habit for complete delivery... D6 Any...had the habit to deliver...did deliver the money to clerk H. who completely... CONCLUSION D7 Driver S did deliver the money to clerk H. Figure 37. DCIT inference template of American Express (defendant’s first inference line).  A Generalizable Argument Structure 149 DEFENDANT’S 1ST INFERENCE LINE Subject phrase Predicate phrase D8 Driver S...had a signed receipt admitting the delivery by him. D9 Any...had a signed receipt admit-...did deliver the money to clerk H. who ting the delivery by him... CONCLUSION D7 Driver S did deliver the money to clerk H. Figure 38. DCIT inference template of American Express (defendant’s second inference line). Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 PLAINTIFF’S 1ST OFF-LINE DIVERTING OBJECTION Subject phrase Predicate phrase P1 Driver S...did not, according to clerk H, deliver the money to clerk H. P2 Any...did not, according to clerk...did not deliver the money to who H, deliver the money to clerk clerk H. H... CONCLUSION P3 Driver S did not deliver the money to clerk H. Figure 39. DCIT inference template of American Express (plaintiff’s first off-line diverting objection). PLAINTIFF’S 2ND OFF-LINE DIVERTING OBJECTION Subject phrase Predicate phrase P4 Driver S...stole, according to F, from com- pany packages. P5 Any...stole, according to F, from...did steal from company packages. who company packages... P6 Any...did steal from company did not deliver the money who packages... to clerk H. CONCLUSION P3 Driver S did not deliver the money to clerk H. Figure 40. DCIT inference template of American Express (plaintiff’s second off-line diverting objection). 150 A Generalizable Argument Structure PLAINTIFF’S IN-LINE BLOCKING OBJECTION Subject phrase Predicate phrase P7 Driver S...did not, according to clerk H, habitually deliver completely. P8 Any...did not, according to clerk...did not habitually deliver com- who H, habitually deliver com- pletely. pletely... P9 Any...did not habitually deliver...did not deliver the money who completely... to clerk H. CONCLUSION P3 Driver S did not deliver the money to clerk H. Figure 41. DCIT inference template of American Express (plaintiff’s in-line blocking objection). Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 As the Wigmore example (Figure 36) illustrates, probative relevancy can also be an issue when trying to attack and defeat arguments that allegedly support the ultimate probandum. From a DCIT perspective, such attacks fall into one of the three categories. The first type of attack is directed at the design of the argument structure. It contends that the proposed item of evidence offered by the opponent has no probative relevance, since it does not fit within a structurally correct argument attached to the ultimate probandum. The use of a DCIT diagrammatic structure makes it easier to depict this type of objection. The other two types of attacks, while ignoring the argument structure, attempt to reduce or eliminate the probative force of the judge’s acceptability directed towards the ultimate probandum. This is accomplished by either (i) diverting or (ii) blocking, to some degree, the flow of the probative force of acceptability. Figure 42 illustrates, with implicit premises, a diverting objection (off-line) that connects directly to the subject phrase of the ultimate probandum. This can be considered an off-line objection, since it bypasses the existing line of the opponent’s reasoning and presents an alternative chain of phrase predicates leading to an alternate ultimate probandum. This off-line type of diverter falls within Pollack’s classification of rebutting defeaters. Figure 43 illustrates another diverting objection (in-line) that operates within the existing line of reasoning. And Figure 44 illustrates a blocking objection. These last two types fit within Pollack’s classification of undercutting defeaters. By demonstrating precisely how these attacks connect to the line of reasoning of the opponent, their probative relevancy can be established. is included in [assumptions] is included in [assumptions] the class of... the class of... [uni-directional [uni-directional] Figure 42. DCIT inference template of off-line diverting objection.  A Generalizable Argument Structure 151 Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 is included in [assumptions] is included in [assumptions] the class of... the class of... [uni-directional] [uni-directional] Figure 43. DCIT inference template of in-line diverting objection. The acceptability is included in [assumptions] is blocked to some the class of... degree. [uni-directional] Figure 44. DCIT inference template of blocking objection. In depicting the argument structure to the court, it is important to distinguish between convergent and linked arguments [29, p. 278]. Twardy discusses the struggles that students have in making this distinction. There are various tests proposed to make this determination [32, p. 80, 35]. For example, Walton [30, p. 151] proposes the blackout test. When considering two premises, if removing (i.e. blacking out) one of them causes a significant reduction of acceptability, then the premises are linked. 152 A Generalizable Argument Structure The test from a DCIT perspective is, perhaps, more definitive. Any premise connected along the same line of nested classes (e.g. line A or B in Figure 45) is linked in relation to any other premise along the same transitive reasoning path. So, if the phrase predicate can appropriately be nested between the classes of phrase predicates based on class-inclusion, or supports such inclusion as an assumption, there is a linkage between the premises. Any premises that exist on separate lines of nested classes (e.g. one on inference line A and one on inference line B in Figure 45) that separately join the subject phrase and predicate phrase of the same conclusion are convergent (Figure 45). Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 is included in [assumptions] the class of... [uni-directional] Figure 45. DCIT inference bridge diagram of multiple lines of inference. As an additional issue, when working in the legal domain, as discussed previously, the argument structure needs to account for the defeasible nature of many of the arguments used in law [32, p. 29]. This means that the fluid context of new facts, exceptions and assumptions within which the argument exists must be represented. This is done by reflecting in the structure necessary and adjunct assumptions that are inherent in any of the premises to account for the possibility of new facts, exceptions and degrees of adjunct support. A necessary assumption, indicated by [N] in the DCIT template, is one whose removal causes the premise it supports to fail. An adjunct assumption, indicated by [A], is one that provides collateral support (e.g. The witness was unbiased), but whose removal only weakens the premise it supports. The distinction between adjunct and necessary is important when considering probative relevancy. The lack of acceptance of a necessary assumption can defeat the claim of probative relevancy since the argument structure fails. The lack of acceptance by the court of an adjunct assumption, however, does not defeat a claim of probative relevancy. It only affects the probative weight bearing capacity of the structure. For example, that fact that a witness was biased does not automatically completely negate the witness’s testimony. In addition to the explicit indication of assumptions in the DCIT structure, a companion understanding of different types of generalizations is important to navigate in the courtroom. A universal generalization is the type used in deduction [32, p. 29]. An inductive generalization  A Generalizable Argument Structure 153 of the statistical variety, while not ensuring deductive validity, can be ‘inductively strong’ [32, p. 30]. A defeasible generalization is about what ‘may generally be taken to be true, subject to exceptions’ [32, p. 30]. A defeasible generalization is used for presumptive (i.e. plausibilistic) reasoning in which assumptions are more typically considered. For example, the following ‘fled from the scene of a crime’ example, Figure 46, illustrates some of these assumptions that support the premise that ‘anyone who fled from the crime scene according to witness A, actually fled from the crime scene’. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 is included in the class of... [assumptions] [uni-directional] Figure 46. DCIT inference bridge diagram with premise assumptions. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase 1 The boy...fled from the crime scene according to witness A. 2 Any...fled from the...actually fled 1. [N] Witness A was in a who crime scene from the crime position to observe. (that) according to scene. 2. [A] Witness A is unbiased. witness A... 3. [N] Witness A had the capacity to remember the incident. 3 Any...actually fled...exhibited sus- who from the crime picious behavior (that) scene... to some degree. 4 Any...exhibited...was lawfully who suspicious detained. (that) behavior to some degree... CONCLUSION 5 The boy was lawfully detained. Figure 47. DCIT inference template with premise assumptions. 154 A Generalizable Argument Structure The argument in Figure 47 is closely related to argument schemes. These are pre-formulated stereotypical argument structures containing prescribed premises along with companion assumptions. For probative relevancy determinations in litigation, the difficulty with argument schemes is that the judge must be familiar with the exact argument scheme since the linkage between the premises and the conclusion is not necessarily immediately obvious. For example, the argument scheme for Argument from Position to Know is as follows [32, p. 37]: ‘Position to know premise: a is in a position to know whether A is true or false. Assertion premise: a asserts that A is true (false). Conclusion: A may plausibly be taken to be true (false). Critical Questions (i.e. related assumptions) 1. Is a in a position to know whether A is true? 2. Is a an honest (trustworthy, reliable) source? Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 3. Did a assert that A is true (false)?’ When this argument scheme is translated into a DCIT structure, the linkages between the premises become immediately apparent (Figure 48) through the transitive relationship. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject Predicate phrase phrase 1 A...is asserted to be true (false) by a. 2 Any is as-...is true (false). 1. [N] a was in a position to who serted to know. (that) be true 2. [N] a has the capacity to (false) by remember correctly. a... 3. [A] a is an honest (trust- worthy, reliable) source. 4. [A] Cognitive biases of a have been appropriately considered. CONCLUSION A is true (false). Figure 48. DCIT inference template of ‘Position to Know’ argument scheme. Unlike the nested linkage of phrase predicates which makes the logical connection obvious if the item of evidence is one of the transitively linked premises, however, the statement form of the assumptions within the DCIT argument structure does not have the same obvious linkage. If the item of evidence offered for admission, for example, is a claim that the witness was not capable of perceiving the event (e.g. The boy fled the crime scene), the connection to the ultimate probandum (e.g. The boy was lawfully detained) may initially rely upon the court’s acceptance of this connection from common knowledge. If this connection is not apparent to the court, the attorney can set up another argument structure with a string of phrase predicates making the main conclusion that the alleged  A Generalizable Argument Structure 155 fact that the witness was unable to perceive the event is relevant to the ultimate probandum (e.g. The boy was lawfully detained). In addition to a structurally correct argument containing both the item of evidence and the ultimate probandum, every necessary premise within the shared argument structure must have some degree of acceptability, as determined by the court [29, p. 181]. This second requirement raises the topic of probative force or probative weight which is the quality that can increase or decrease the acceptability (e.g. probability) of the main conclusion. Walton [28, p. 115] describes two factors that create probative weight: ‘In the case of each single inference, the premises, and the structure of the inference itself, will have what could be called a “probative function” of increasing the probative weight of the conclusion, depending on two factors. One is how probable the premises are. The other is how strong the link is between the premises and the conclusion’. This typical examination of the probative function by evaluating these two factors, however, lends unnecessary complexity. By using a DCIT argument structure, an unquestioned absolute link between the premises and the conclusion is ensured Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 since there is a defeasible logical necessity. The only requirement remaining, as a result, is to examine the probative function of the individual linked premises and any associated necessary assumptions. With a DCIT approach and perspective, the ‘probative function’ referred to by Walton can be metaphorically described as probative weight bearing capacity. And probative weight can be metaphorically considered as a measure of the amount of acceptability that can reach the main conclusion (e.g. ultimate probandum). For example, consider an argument in which the ultimate probandum is that ‘Harry is not subject to deportation’ (Figure 49). The hiker in Figure 49 represents the judge. And the backpack carried by the judge contains the judge’s total capacity of acceptability. The proponent of the argument wants the judge to perceive the probative weight bearing capacity of the argument capable to handle the full load of acceptability as the judge walks towards the ultimate probandum at the other side of the inference bridge over the expanse of uncertainty. The use of the judge as the carrier of the acceptability reflects the typically subjective nature applicable to this assessment. For example, consider evaluating whether the evidence ‘Any who is identified by the British Nationality Act as a British subject is a British subject’ (Figure 49) has any probative relevancy. First, it is shown to be contained within a structurally correct argument since it fits within the DCIT structure which connects to the ultimate probandum. But the probative weight that can reach the ultimate probandum depends on each necessary premise evaluated by the judge as being capable of supporting at least some amount of probative weight. If, for example, the necessary assumption that ‘The Act is legally in effect’ was believed by the court to be false, then no amount of acceptability could pass over the span supported by that assumption to reach the ultimate probandum. Essentially, the weakest component in a single inference bridge determines the level of acceptability (i.e. probative weight) that can reach the ultimate probandum. Walton [28, p. 112] refers to this principle as the ‘least plausibility rule’ applicable to linked arguments. One approach in attempting to increase the perceived probative weight bearing capacity of a necessary premise is to add qualifiers that more precisely state the likelihood or probabilities attached to the premise. This inference bridge perspective (Figure 49) also makes the DCIT concept of an inference step apparent. From a DCIT perspective, an inference step is the transitive substitution that the main conclusion subject phrase makes in the place of each adjoining predicate phrase as the subject phrase moves to connect to the predicate phrase of the main conclusion. For example, Figure 50 shows three inference steps (i.e. transitive substitutions). Unzipping the ultimate probandum and unpacking some of its predicates phrases that are implicit within the ultimate probandum also illustrate that the probative weight bearing capacity of the argument structure does not necessarily decrease with more inference steps. If the court determines 156 A Generalizable Argument Structure Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 is included in [assumptions] the class of... [uni-directional] Figure 49. DCIT inference bridge (lateral view) diagram of ‘Harry is not subject to deportation’. 1 2 3 inference step is included in the class of... [uni-directional] [assumptions] Figure 50. DCIT inference bridge (lateral view) diagram depicting inference steps. that each span can bear a full load of acceptability, multiple spans do not affect the probative weight bearing capacity of the argument structure. And intuitively, perhaps, if any span is determined to have a full probative weight bearing capacity, then any further granulation of that premise should not reduce this full probative weight bearing capacity. To illustrate the applicability of DCIT in court, the following court’s analysis of probative relevancy in State of Oregon v. McNeely, 330 Or 457 (2000) is translated into a DCIT format as shown in Figures 51–56. Defendant contends, in the alternative, that the trial court erred in denying his motion to exclude Thompson’s testimony, because Thompson was unable to identify defendant at trial as the man with whom he had spoken in jail …. Defendant objected, arguing that because Thompson was unable to identify defendant, his testimony was irrelevant … The state responds that Thompson’s  A Generalizable Argument Structure 157 testimony was ‘conditionally relevant,’ citing OEC 104, 5 and, thus, was properly admitted... Conditional relevancy means a situation where one fact is relevant only if another fact is proven … We review to determine whether there was sufficient evidence for the trial court to have submitted the issue to the jury... When dealing with a matter of conditional relevancy under OEC 104(2), the judge determines whether the foundation evidence is sufficient for the jury reasonably to find that the condition on which relevance depends has been fulfilled … At trial, Thompson testified that he had spoken with a man in jail who had admitted choking and killing the victim. If defendant were that man, then Thompson’s testimony was relevant evidence. There also was evidence at trial that Thompson and defendant had met in jail in 1993. Thompson testified: ‘I spoke to somebody that represented himself as being [defendant] or was represented by somebody else as being [defendant].’ … Thompson related several incriminating conversations that he had had with that man. Moreover, there also was evidence that defendant had gained 25 pounds and had shaved off his moustache since the time when he and Thompson Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 were in jail together … Despite Thompson’s inability to identify defendant at trial, the trial court determined that a reasonable juror could find that defendant was the person with whom Thompson had spoken in jail. The record supports that conclusion. We agree with the trial court. Thompson’s inability to identify defendant at trial went to the weight the jury might give to his testimony, not to its admissibility. It follows that the trial court did not err in leaving the matter to the jury. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase P1 Thompson’s represented that a testimony man identified by himself or some- body else as the defendant admit- ted to choking and killing the victim. P2 Any represented that has a tendency to P4 1. [N] The man identi- who a man identified make defendant’s fied as the defendant (that) by himself or guilt more prob- actually was the defen-... somebody else able. dant. as the defendant admitted to choking and killing the victim. P3 Any has a tendency is relevant. who to make defen- (that) dant’s guilt... more probable CONCLUSION P5 Thompson’s testimony is relevant. Figure 51. DCIT inference template of ‘Thompson’s testimony is relevant’. 158 A Generalizable Argument Structure DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase D1 The defen- could not be dant visually identi- fied, at the pre- trial, by Thomp- son as the person who admitted to the murder. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 D2 Any could not be was not the D3 1. [N] The defendant’s ap- who visually iden- person who pearance had not significantly (that).. tified, at the admitted to the changed from the time of the. pretrial, by murder. admission. Thompson as the person who admitted to the murder. CONCLUSION D4 The defendant was not the person who admitted to the murder Figure 52. DCIT inference template of ‘The defendant was not the person who admitted to the murder’. DEFEASIBLE CLASS-INCLUSION TRANSITIVITY Premise Assumptions Subject phrase Predicate phrase P5 The defendant had gained 25 pounds and shaved his mous- tache since the admission. P6 Any had gained 25 had significantly who pounds and changed his (that)... shaved his appearance. moustache since the admission CONCLUSION P7 The defendant had significantly changed his appearance. Figure 53. DCIT inference template of ‘The defendant had significantly changed his appearance’.  A Generalizable Argument Structure 159 Plaintiff subject phrase arrow = transitive step P1 predicate judge phrase P4 P2 final predicate Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 phrase P3 is included in the class of... [uni-directional] [assumptions] P5 Figure 54. DCIT inference bridge diagram of ‘Thompson’s testimony is relevant’. Defendant subject phrase arrow = transitive step D1 predicate judge phrase final predicate phrase D2 is included in the class of... D3 [uni-directional] [assumptions] D4 Figure 55. DCIT inference bridge diagram of ‘The defendant was not the person who admitted to the murder’. 160 A Generalizable Argument Structure Defendant subject phrase arrow = transitive step P5 predicate judge phrase final predicate phrase P6 is included in the class of... Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 [uni-directional] [assumptions] P7 Figure 56. DCIT inference bridge diagram of ‘The defendant had significantly changed his appearance’. In conclusion, the relative lack of strict logically rigour in typical court proceedings runs counter to the demand for logical rigour for determining the probative relevancy of evidence. Removing the issue of structural correctness through the use of DCIT simplifies this determination. And in my own professional litigation experience using DCIT during the last 3 years, I have found a DCIT argument structure useful in persuading the court. This structural clarity does, however, come with a resource cost. An argument presented to the court may first need prior regimentation to fit within the DCIT form. This requires time and some specialized knowledge on the part of the attorney. On the other hand, the court need not share in this specialized knowledge since evaluating a DCIT argument is easier than designing one. Further, the resulting argument transparency that results from DCIT can help eliminate the purposeful use of obfuscation. This transparency is particularly evident if argument diagramming (i.e. argument mapping) is used to depict the DCIT structure. And, further, more correct judicial determination in other types of rulings may be possible as the use of DCIT is extended to other areas of argumentation in litigation. Its simplicity in structure may also increase the functionality of computational methods that are based on its algebraic formulation. Acknowledgements The author gratefully acknowledges Tim van Gelder for his valuable guidance in the practice of argument mapping during my years in association with him at Austhink™; my Lewis & Clark Law School “Advanced Argumentation” students for their intellectual curiosity and eagerness to explore new ideas of inference; Peter Tillers for his encouragement to me to explore less conventional concepts of inference; Sharone Lee for our ongoing discussions of the placement and utility of fact-based inquiry within the dimensional structures of knowledge; Doug Carter for our ongoing  A Generalizable Argument Structure 161 discussions on ways to help make learning DCIT easier; and, David Hitchcock for spotting the need for additional assumptions in an important example. References T. Anderson, D. Schum and W. Twining. Analysis of Evidence, 2nd edn. Cambridge University Press, 2005. I. Angelelli. Predication theory: classical vs modern. In Relations and Predicates, H. Hochberg and K. Mulligan, eds, pp. 55–80. Ontos, 2004. Aristotle. Categoriae. In Aristotelis Categoriae et liber de interpretatione, L. Minio-Palueelo ed. 1949. Downloaded from http://logcom.oxfordjournals.org/ by guest on March 9, 2015 N. B. Cocchiarella. Logic and ontology. Axiomathes, 12, 117–150, 2001. J. Deneault and M. Ricard. The assessment of children’s understanding of inclusive relations: transitivity, asymmetry, and quantification. Journal of Cognition and Development, 7, 551–570, 2006. G. Englebretsen. Three Logicians: Aristotle, Leibniz, and Sommers and The Syllogistic. Van Gorcum & Company, 1981. G. Englebretsen. Line Diagrams for Logic: Drawing Conclusions. The Edwin Mellen Press, 1998. J. B. Freeman. Systematizing Toulmin’s warrants: an epistemic approach. Argumentation, 19, 331–346, 2005. L. Groarke. The fox and the hedgehog: on logic, argument, and argumentation theory. Proto Sociology, 13, 29–45, 1999. D. Gooden and D. Walton. Defeasibility in judicial opinion: logical or procedural. Informal Logic, 28, 6–19, 2008. J. Hage. Law and defeasibility. Artificial Intelligence and Law, 11, 221–243, 2003. J. Hintikka. Analyses of Aristotle. Kluwer Academic Publishers, 2004. D. Hitchcock. Good reasoning on the Toulmin model. Argumentation, 19, 373–391, 2005. R. H. Johnson. Making sense of “informal logic”. Informal Logic, 26, 231–258, 2006. G. Lakoff and M. Johnson. Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought. Basic Books, 1999. J. Laronge. Visualizing Probative Relevancy: Transitive Chains v. Tree-like Structures. Unpublished manuscript, 2006. J. Laronge. Argument pyramid, 2007. http://www.inferencepath.edublogs.org. R. C. Pinto. Evaluating inferences: the nature of role of warrants. Informal Logic, 26, 287–317, 2006. J. Pollack. Cognitive Carpentry. MIT Press, 1995. F. Sommers. Ratiocination: an empirical account. Ratio, 21, 115–133, 2008. F. Sommers and G. Englebretsen. An Invitation to Formal Reasoning. Ashgate Publishing Company, 2000. S. Toulmin. Uses of Argument. Cambridge University Press, 1958. C. Twardy. Argument maps improve critical thinking. Teaching Philosophy, 27, 95–116, 2004. W. Twining. Theories of Evidence: Bentham & Wigmore. Stanford University Press, 1985. W. Twining. Rethinking Evidence: Exploratory Essays, 2nd edn. Cambridge University Press, 2006. 162 A Generalizable Argument Structure T. van Gelder. Enhancing deliberation through computer-supported argument visualization. In Visualizing Argumentation: Software Tools for Collaborative and Educational Sense-making, P. Kirschner, S. Buckingham Shum and C. Carr, eds, pp. 97–115. Springer, 2002. T. van Gelder. The rationale for rationale™. Law, Probability & Risk, 6, 23–42, 2007. D. Walton. Legal Argumentation and Evidence. The Pennsylvania State University Press, 2002. D. Walton. Relevance in Argumentation. Lawrence Erlbaum Associates, Inc., 2004. D. Walton. Fundamentals of Critical Argumentation. Cambridge University Press, 2006. D. Walton. Dialog Theory for Critical Argumentation. John Benjamin Publishing Company, 2007. D. Walton. Witness Testimony Evidence: Argumentation, Artificial Intelligence, and Law. Cambridge University Press, 2008. J. H. Wig