LA VIDA DEL GOBERNANTE 4 PNG, soportes del Altar 2

We noted in section 6.1.1that conventional logic focuses on the meaning attached to quantifiers like FORALL and logical connectives like IMPLIES and provides rules

so that arguments employing these can derive valid conclusions no matter what meanings are attached to the other “nonlogical” terms appearing in the argument. Toulmin [121] observes that this privileges a certain kind of reasoning and neglects others that may be more useful and important in the real world. In particular, the deductive IMPLIES is about certainty, whereas in daily life we often assert more nuanced relations among terms and qualify implications with words like “probably,” “possibly,” “presumably” and so on, or we say merely “this suggests that.” One of Toulmin’s examples, which may be compared to the syllogism (3) is the following.

Premise 1 : Scarcely any Swedes are Roman Catholics Premise 2 : Peterson is a Swede

Conclusion : Almost certainly, Peterson is not Roman Catholic

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This introduces the idea of an inductive argument, in which truth of the premises does not (as in a deductive argument) guarantee truth of the conclusion, but supports it with various degrees of force. But once we abandon the framework of deductive logic, we lose its deep metatheory, its algorithms, and its tools. There are approaches that try to reconcile logic with less-than-certain inference, such as probabilistic and Markov logics, but Toulmin had a different goal. He sought to develop a style of argument that more closely integrated our knowledge of a subject and our reasoning about it—in contrast to deduction, where the logic and the subject matter of an argument are separated.

Toulmin’s motivation derived from philosophy and epistemology (i.e., to chal- lenge the primacy of deductive reasoning) but his work was adopted by some of those working in rhetoric, law, and other fields that concern real-world arguments. Those who first developed the ideas of safety cases were conscious that absolute certainty is unattainable, for it is impossible to know everything that might affect the safety of a system, and so they, too, drew on Toulmin’s approach.

(Argument) (Evidence) Backing Grounds Qualifier Claim Rebuttal Warrant subclaim Grounds (Evidence)

Figure 10. Toulmin’s Model of Argument

Toulmin’s model of argument has the following six elements (the descriptions are taken from [2]), which are also portrayed in Figure10.

Claim: This is the expressed opinion or conclusion that the arguer wants accepted by the audience.

Grounds: This is the evidence or data for the claim.

Qualifier: An adverbial phrase indicating the strength of the claim (e.g., certainly, presumably, probably, possibly, etc.).

Warrant: The reasoning or argument (e.g., rules or principles) for connecting the grounds to the claim.

Backing: Further facts or reasoning used to support or legitimate the warrant. Rebuttal: Circumstances or conditions that cast doubt on the argument; it repre-

sents any reservations or “exceptions to the rule” that undermine the reasoning expressed in the warrant or the backing for it.

Figure10portrays a single argument step and suggests how these can be chained together, with the (sub)claim at one level providing the grounds (evidence) at a higher level. Toulmin’s original formulation did not anticipate this hierarchical form and used a less symmetrical graphical representation; explicit chaining of argument steps seems to be due to Newman and Marshall [87].

If we were to rotate Figure 10 through 90 degrees counterclockwise, it would closely resemble Figure 5, which portrayed the basic argument step used in CAE notation. This is no accident for, as noted, the developers of CAE and GSN explicitly acknowledge a debt to Toulmin. The claim, grounds, and warrant of Toulmin’s approach correspond to the claim, evidence, and justification of an argument step in an assurance case.

Toulmin’s qualifier seems not to be employed in assurance cases, even in those frameworks such as GSN (and, to a lesser extent, CAE) that explicitly endorse inductive (i.e., less than definitive) reasoning. Our opinion is that any assurance case that is not fully deductive should employ qualifiers to indicate for each reasoning step whether that step should be interpreted deductively (i.e., the premises imply the conclusion) or inductively (i.e., the premises suggest the conclusion).

Toulmin’s backing seems to function rather like a confidence item in an assurance case: that is, it provides additional reasons why we should believe the claim, while the rebuttal is rather like a negated assumption (i.e., it specifies conditions under which the argument step does not apply).

Toulmin’s approach is often used in both teaching and performing the analysis of informal arguments: the idea is to identify the claim, warrant, qualifier, and so on and then consider these within Toulmin’s framework. Adelman and colleagues conducted an empirical evaluation of such an application of Toulmin’s approach in which subjects were asked to evaluate the soundness of arguments presented in two concocted “magazine articles” [2]. The results were inconclusive, and the authors suggest “one needs to be cautious of the claimed value of structured argumentation tools employing the Toulmin formalism.” This particular experiment does not seem

well-aligned with possible use of Toulmin’s approach in assurance cases, but the suggestion of caution is appropriate.

The case that Toulmin advances against classical, deductive logic has some ap- peal when the topics of discourse are ethics, religion, or aesthetics, say, but it is less persuasive for the topic of assurance (though Cassano and Maibaum provide a sympathetic account [14]). There will certainly be areas of doubt in an assurance case, and human judgment and experience may be the appropriate recourse, but these doubts concern our ignorance or uncertainty about the world (i.e., the formu- lation of our premises) and do not require reformulation of the notion of logic (i.e., rejection of the idea that validity of the reasoning in an argument can be separated from the truth of its subject matter). This is different than arguments in ethics, for example, where the entire basis for debate may be contested and reasonable people may come to different conclusions.

There are several systems that provide support for representation and evaluation of human arguments using Toulmin’s model. Araucaria is one that is widely-cited and seems well-supported [99]; it is available at http://araucaria.computing. dundee.ac.uk/. Araucaria also supports other styles of human argument and is able to represent arguments using various forms of diagram [100].