EVALUACIÓN DE IMPACTOS AMBIENTALES (VALORACIÓN I = I + E + M + P + R)

For a long time, formal logic was the method of choice to study arguments. The formal-logical approach requires that arguments are represented as expressions of a formal language, for instance, as sentences of propositional calculus. These sentences can be analyzed in terms of their logical properties, for instance, whether a given argument represents a deductively valid inference. To analyze natural language arguments using the formal-logical approach, one has to apply a number of abstractions to ultimately arrive at a formal expression. Table 3 demonstrates the process based on an example from van Eemeren et al. (1996).

The example demonstrates that formal logic deals with expressions that are reduced to their bare logical core. Many aspects that may be of interest to an argument analyst are stripped of from the original natural language statement or dialogue in the process of abstraction (e.g., linguistic, contextual, social, and psychological aspects are lost).

Besides this traditionally-oriented approach, other formal-logical approaches exist nowadays that are specifically tailored to model and analyze argumentative discourse. For instance, Barth and Krabbe’s (1982) approach of formal dialectics yields a formalism to model a critical dialogue between a proponent and opponent in terms of general dialogue rules, an initial thesis, initial (and ongoing) concessions made by the discussants, attacking and defending moves, and conditions for winning the dialogue game. The presented calculus allows proving, with mathematical rigor, that an initial thesis can (or cannot) be established in light of a set of initial concessions made by an opponent (equivalent to the existence of a winning strategy of the proponent). The approach has been criticized to reduce dialogues to existing formal systems, rather than extending existing formal systems with pragmatic notions to better account for real-world dialogues (Stock 1982).

Table 3

Formal-logical analysis: From natural language argument to propositional argument form

Analysis step description

Example analysis Comment

(1) Original transcript

of conversation Dale: Mary said she was going to get beef or cod. Do you know what we’re eating

tonight?

Sally: No, but if she’s already done the shopping it’ll probably be in the fridge. I’ll have a quick look in the fridge … It’s stacked full. But I can’t smell fish, anyway.

Dale: O.K., as I see it, it is beef tonight since it was either that or cod and there is no fish. (*)

The statement to be analyzed is marked with an asterisk (*)

(2) Make reasoning explicit including all implicit elements

Dale: It was either beef or cod. There is no fish. If there is no fish, we are not going to eat cod. Therefore, it is beef tonight.

Makes the argument complete and self-contained

(3) Standardize representation by omitting references to persons, using uniform wording, and marking of premises and conclusion

premise: We are going to eat beef or we

are going to eat cod.

premise: There is no fish.

premise: If there is no fish, we are not

going to eat cod.

conclusion: We are going to eat beef.

(4) Replace natural language clauses with

sentence constants

while keeping words that define the

sentence logic (or, not,

and)

premises: B or C, not F, if not F then not C conclusion: B

B = We are going to eat beef C = We are going to eat cod F = There is fish

(5) Replace logic- related keywords with

logical constants 𝐵 ⋁ 𝐶 ¬ 𝐹 ¬ 𝐹 → ¬ 𝐶 /∴ 𝐵 ⋁ = or ¬ = not X → Y = if X then Y /∴ = therefore (conclusion) (6) Determine whether a valid general

argument form exists,

which the specific argument is an substitution instance of 𝑝 ∪ 𝑞 ¬ 𝑟 ¬ 𝑟 → ¬ 𝑞 /∴ 𝑝

Argument is valid since corresponding valid argument form exists

Other more recent developments include the field of computational dialectics (Gordon 1996), which tries to formalize argumentative reasoning, e.g., to implement conflict-resolution behavior in multi-agent systems or support strategies in mediation systems for online discussions. One particular class of logical systems, non-

monotonic logics, has been identified as particularly relevant to model argumentation

(Gordon et al. 2007). In classical, monotonic logic, the set of sentences entailed by a theory (or knowledge base) does monotonically increase when new axioms are added to the theory. Adding axioms that do not contradict the theory only allows inferring new sentences; adding axioms that contradict the theory makes the theory inconsistent, meaning that any sentence can be inferred. Non-monotonic logic systems, on the other hand, allow defeasible inferences. Adding new sentences to a theory can defeat existing inferences, that is, previously, prima facie, justified sentences may be withdrawn again. Similarly, argumentation may be considered as a non-monotonic process since statements and inferences accepted at one point can be withdrawn again when new arguments or evidence are presented. Gordon et al. (2007) criticize the static nature of non-monotonic models of argumentation and propose their own formal model, Carneades, which takes procedural aspects into account. In particular, Carneades allows modeling, on a statement-by-statement basis, the current dialectical status (i.e., statement is stated, questioned, accepted, or rejected), the allocation of the burden of proof (i.e., which party is obliged to substantiate a statement), and the proof standard that applies (i.e., the rules that decide whether a statement is acceptable or not; e.g., “scintilla of evidence,” or “best argument”). This information can be employed to model important procedural aspects, such as the overall procedural context (e.g., in criminal trials, a defendant’s guilty must be proven with evidence “beyond reasonable doubt”), the current procedural stage (e.g., at the beginning of a deliberation dialogue, when brainstorming ideas, one may apply a low standard of proof), changing dialectical statuses (e.g., conceding to a statement of the other party alters its dialectical status to “accepted”), and changing obligations of involved parties (e.g., questioning an implicit assumption of an argument typically shifts the burden of proof back to the originator of the argument).