esta fila y las siguientes se utilizan para combinar condiciones

In order to analyse the validity of an argument it is necessary to first resolve the conflicts in which the argument is involved. Settling a conflict involves determining which argument is most persuasive. If an argument is “better” than an opposing argument it is said to be stronger. In real world argumentation the audience measure the strength of arguments and decide which is strongest.

Within an argumentation framework it is the fourth layer that performs this task. It examines all conflicts in the argumentation process and, for each conflict, attempts to decide which argument wins. Resulting in a series of binary relationships each stating that argument X is in conflict with, and stronger than (or at least as strong as), argument Y :

is important to note that this relation does not yet tell us with what arguments a dispute can be won; it only tells us something about the relative strength of two individual conflicting arguments. The ultimate status of an argument depends on the interaction between all available arguments ([38] page 13)

This subsection discusses defeat in terms of individual conflicts, and not the overall status of the arguments. It is the the fifth layer of the framework that awards a status to individual arguments. It does this by creating a network (argument graph) through which it is able to determine which arguments are defeated, which are reinstated, and which are undefeated. More details on this can be found in Section 2.4.6.

Returning to the notion of defeat between pairs of arguments, Prakken and Vreeswijk [38] state that there are two basic forms of defeat: weak and strict. Weak defeat occurs when the attacker is not weaker than the argument being attacked. Where the arguments are the same strength they defeat each other thus cancelling each other out. Strict defeat describes the situation where the attacking argument is stronger than the attacked argument - the attacked argument is defeated, and the attacker is unblemished. For instance, if argument A is weaker than argument B it cannot rebut or undercut it successfully; however, B can undercut and/or rebut A. Some frameworks, e.g. Prakken and Sartor [71], deem that assumption attacks and undercuts always work, thus only rebuttals require the individual argument strengths to be compared. Prakken and Sartor justify this on the basis that it is the reality in their chosen application domain, law.

A feature of Prakken and Sartor [71] is that they use both strict and defeasible inferences. A strict inference can produce a strict argument that cannot be defeated. However, any argument that contains a defeasible inference, or piece of defeasible information, is automatically defeasible even if the rest of the argument is strict.

Conflict resolution

Generally speaking there are two paradigms for conflict resolution. In the first the conflicting arguments are compared in isolation. Arguments are balanced with all related (supporting and attacking) arguments in the second approach.

As an example of the latter technique Pollock [69] documents the idea that several weak arguments can combine to defeat a single strong argument, so-called collaborative defeat. In an extension of this idea, an argument that is weaker than an opponent can still diminish that opponent. Both of these approaches rely on the arguments having an associated strength.

Additionally, the concept of strength is utilised when arguments are compared directly. An argument can defeat another if it is at least as strong as it (weak defeat ); being stronger than the other argument results in strong defeat.

In Pollock [69], each component of an argument (premise, inference rule, sub- argument) has a weight assigned to it, indicating the degree of confidence in that component. Subsequently, the weakest link principle is used to aggregate these weights to produce a single score for the global argument. This principle captures the idea that an argument is as strong as its weakest component, and thus the lowest weight from the components is assigned to the global argument. An alternative mechanism is the last link principle - the argument’s strength is equivalent to the strength of the final inference rule used in the argument’s creation. Krause et. al. [74] propose that the weight of an individual argument could be a probability, and thus the strength of the global argument computed using probability calculus.

Another mechanism to compare arguments in isolation is the notion of preferences. Instead of computing the individual strengths of arguments, this mechanism decides that one argument is preferable to another. This is done on the basis of a list of binary relations indicating a preference between arguments, often on the basis of a preference between premises and/or inference rules in the arguments. Such systems, called preference-based argumentation frameworks [75], are an extension of Dung’s framework and only allow one argument to strictly defeat another if it is preferred over it. Prakken and Sartor [71] take the notion of preferences a step further by allowing them to be the subject of argumentation.

A popular mechanism for calculating such preferences is specificity - the most specific argument wins any conflict [76]. Simari and Loui [76] calculate their preference order using implicit information from the knowledge base. It is possible that the original data source has an explicit degree of confidence associated with the data, and this could be used in the creation of a preference ordering.

Many argue that the mechanism for deciding between arguments should be domain specific [77, 71]. For example, only a legal application will apply principles such as lex posterior which captures the notion that newer laws override earlier ones.

An alternative to preference-based frameworks is value-based argumentation frame- works [78]. These extend Dung’s framework by taking account of Perelman and Olbrechts-Tyteca’s notion of audience [17]. Arguments are evaluated based on the values and beliefs of individual audience members. Value-based systems ensure at- tacks only succeed if the value promoted by the attacker is preferred to the value promoted by the attacked; however, the success is relative to each individual in the audience as each person is likely to have their own preference ordering for the values. For example, a medic will believe effective treatment is more important than cost- effective treatment, and thus accept arguments that promote the notion of effective treatment when they are attacked by arguments that promote a cheaper, less effective alternative.