Central to argumentation theory is the notion of an argument. This term is overloaded, with many domains having specialised meanings - in computer science, an argument is the name given to a piece of input passed into a program or sub-program. These definitions shall be ignored in this thesis.
Even within argumentation theory the term argument has a very broad range of definitions, and thus usages, as illustrated by:
There are, as might be expected, almost as many definitions of argument as there are argument theorists. At one end, the all-encompassing tax- onomy of Gilbert [46] covers a panoply of situated action that can count as argument, from artistic creation, through non-lingustic communication, to physical activity. At the other end, van Eemeren and Grootendorst’s pragma-dialectics [24] associates argument with the notion of critical dis- cussion, a closely bounded, tightly specified linguistic activity whose defi- nition rests upon speech act theory. ([47] page 4)
As there is no canonical meaning, in this work the definition of argument will be a reason to believe something is true. Examples include a reason to believe a gene is expressed in a tissue, or a mathematical proof of a formula.
Often in disciplines with philosophical roots, such as AI, arguments are composed from propositions. Propositions are statements that can be evaluated to be true or false, e.g. it is raining. One proposition is taken to be the claim (or conclusion) of the argument, i.e. the statement that the argument supports. The remaining propositions are the premises (see Figure 2.2). When all the premises are evaluated to be true, the conclusion is likely to be true. The level of likelihood depends on the class of argument, generally speaking three exist: deductive, inductive, and a third category, which shall be called defeasible in this document.
Figure 2.2: The basic layout of a logical argument.
A simple example of an argument could provide a reason why someone will get wet today:
The weather report said it would rain today, therefore you will get wet.
This argument clearly has a premise (The weather report said it would rain today), and a conclusion (you will get wet ). However, this argument does not provide a link between the premises and the conclusion, i.e. a statement of why the premises imply the conclusion. Often in natural language arguments the link is implicit, in this case:
If it rains, you will get wet.
The weather report said it will rain, therefore you will get wet.
Arguments of this style correspond to the logical inference rule known as modus ponens, which has the basic form: If A then B. Analysis of arguments, and classes of arguments, reveal that this is the pattern of many, perhaps even most, common arguments [48]. Many real world arguments need to be rewritten in order for that arrangement to become obvious - as demonstrated above.
Modus ponens style rules are widely applied in AI, where they are used for forward chaining [49]. Through this mechanism of chaining an individual argument can be used as a part of a bigger argument, see Figure 2.3. Arguments are linked by using the conclusion of one argument as a premise in the second. This can continue indefinitely. However, if any sub-argument is shown to be invalid then the whole argument is invalid.
Figure 2.3: Arguments can be chained.
Argument strength
Earlier in this section, three classes of argument strength are identified: deductive, inductive and defeasible. These classes represent arguments of varying strengths, from the definitely true to the plausibly true. The stronger the argument, the greater the confidence one can have in its conclusion.
Deductive arguments are essentially proofs. They show something is true, i.e. when the premises are true the conclusion must be true. Inductive arguments are based on probability, and thus the premises being true implies the conclusion is prob- ably true. Inductive arguments are weaker than deductive ones as there is a possibility that the premises are true whilst the conclusion is false. The third category is more difficult to classify, one definition is:
forms of reasoning that are often necessary, but are more tentative in nature and need to be judged circumspectly by reserving some doubts. Such reasoning is presumptive and defeasible. This kind of reasoning is only plausible and is often resorted to in conditions of uncertainty and lack of knowledge. ([2] page 10)
An argument is plausible when it appears to be true [50], i.e. plausible inferences seem reasonable, but cannot be verified. Such arguments are the weakest of the three classes.
According to Walton:
A presumption is something that can be accepted by agreement temporar- ily as things go forward unless at some future point in the exchange it is shown to be unacceptable. ([50] page 166)
For example: “innocent until proven guilty”. From the definition, it seems that a presumption is based on a plausibility that in the future may be proven false, thus overturning the presumption.
The term defeasible was introduced to the philosophical world by Hart [51] through his work in law. Traditionally it refers to arguments that are rationally compelling but not deductive. Today its meaning is more restricted:
In recent work, the term defeasible reasoning has typically been limited to inferences involving rough-and-ready, exception-permitting generaliza- tions, that is, inferring what has or will happen on the basis of what normally happens. [52]
This definition suggests that something can be presumed true “on the basis of what normally happens” unless there is an unusual circumstance (i.e. exception) indicating that this is not a normal situation.
There appears to be an overlap between the definitions of presumption and de- feasibility, with both intertwined with the notion of plausibility. A clarification of these terms is beyond the scope of this document. Instead, the third group of argu- ments, lacking the verifiable backing of probability and thus the strength of inductive arguments, shall be called defeasible to emphasise their fragile nature.
Argument acceptability
Earlier, to define argumentation, the following quote was used:
Argumentation is the process of putting forth arguments to determine the acceptability of propositions. ([37] page 1)
According to this quote, the ability to determine if an argument is true or false is central to argumentation. Details of the mechanisms for performing this classification are reserved until Section 2.4.6; however, the abstract notion shall be discussed further in this section.
Acceptable arguments are those that the evaluator (software or human) finds to be correct (true) - as such these are the arguments with which a dialogue can be won. Pollock [53] defines two types of acceptability. Firstly, an argument is justified
if it appears to be acceptable at the current moment. It becomes warranted if the argument would be acceptable if the agent evaluating it had infinite resources to apply. This distinction is not universally employed, with most authors seeming to concentrate on what Pollock calls justified arguments. Terms used to indicate acceptance include valid, undefeated, justified, in force, and, preferred amongst others.
If there are acceptable arguments, intuitively there are some that are unacceptable, i.e. believed to be false. Invalid, defeated, overruled, not in force, and not preferred are some of the terms used to describe this group.
A third group, sometimes called defensible arguments [38], may be added. These are arguments that are neither valid nor invalid.