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A (very) short tutorial

In its current stage of development, Argutia simulates one step of an exchange of arguments between two formal agents. An agent Φ is seen as a couple [ K, X ] of two sets of propositional formulas. Intuitively K is used as a representation of the factual knowledge of the agent, whereas X corresponds to formulas that this agent cannot admit unless they are part of her actual knowledge. In other words, formulas in X delineate negatively the hopes of the agent (since the agent does not admit these formulas), whereas the positive counterpart indeed should correspond to the agent's expectations (the agent accept everything but formulas of X, unless she has to take account of them because there are already part of her knowledge). Agents can generate answers in front of a finite set of propositional formulas: an answer of the agent Φ = [ K, X ] to a set F is a set A composed both of formulas of K and of negated formulas of X, and such that F is not compatible (regarding X-entailment) with the formulas of K. An argument given by the agent Φ facing a formula C is then a couple < S, ¬C > such that S is an answer to C (where ¬C denotes the propositional negation of C). S and C are called respectively the support and the conclusion of the argument. Roughly, given two arguments α and β, α attacks β when its conclusion corresponds to the negation of some part of the support of β. On the other way, α defends β when its conclusion corresponds to some part of the support of β. Note these are only two among several relations that can be defined between two arguments. Now, the way the agent Φ can generate arguments relies actualy on four possible attitudes she may adopt regarding a formula F (outcome of paraconsistency in X-logics, regarding on wether F is or is not compatible with the knowledge of Φ): she can be For this formula, Against it, Puzzled by it, or still Neutral about it. Given an argument α, it is shown that when Φ is Against a subset of the support of α, she can construct at least one argument attacking this argument. When Φ is For a subset of the support of α, she can construct at least one argument defending this argument. Moreover, if Φ is Puzzled by a subset of the support of α, she can construct at least one argument both attacking and defending α. Eventually, if Φ is Neutral about a subset of the support of α, then she has no argument to give about α.

Let see with a simplified (but real) example how Argutia works. Consider the agents Φ and Ψ representing respectively two politicians, competing for a city election, and arguing about wether the managing of waste requires the construction of a burning manufactory or wether alternate solutions exist: Φ = [{WasteManagement, WasteManagement → (WasteIncineration ∨ WasteReprocessing), WasteIncineration → Dioxyn}, {⊥, Dioxyn}] and Ψ = [{WasteManagement, WasteManagement → WasteIncineration}, {⊥, Dioxyn, WasteIncineration → Dioxyn}]. In other words, both agents agree on the fact that they have to consider the question of waste management (WasteManagement belongs to K of both agents), and that they do not accept the production of dioxyn (Dioxyn belongs to X of both agents), but Φ considers that this question can be adressed by the construction of an incinerator as well as by reprocessing (WasteManagement → (WasteIncineration ∨ WasteReprocessing), while for Ψ, there is no other way than constructing an incinerator (WasteManagement → WasteIncineration). Meanwhile, Φ considers that waste management generates dioxin (WasteManagement → Dioxyn), while Ψ is not ready to accept that waste incineration (through modern means) could produce a significant amount of dioxyn (WasteIncineration → Dioxyn is in X). Note that both agents reason in a consistent way (⊥ belongs implicitely to X of both agents). So, then launch Argutia: it will open a window with four tabs: Configuration, Agents (the selected tab by default), Situation, and Arguments.




The Configuration tab allows to define basic parameters such as logical symbols, or still the underlying langage (english or french).




The encoding of the two agents can be done either by filling up the differents fields with the corresponding formulas or by loading a previous encoding via the File menu. For instance, the above example is represented by:




Switching to the Situation tab opens the following empty window, which permits to compute the different attitudes either of the two agents may adopt in front of the knowledge of the other one.




So, let us compute the attitudes of agent Φ in front of K of agent Ψ:




Especially, Φ is Against the formula WasteManagement → WasteIncineration taken in K of Ψ. Once the attitudes of Φ computed, switching to the Argument tab permits to compute the different arguments that Φ can generate by facing the knowledge of Ψ. Hence, clicking on the Generate button, yields the following output:




As expected, Φ can attack the knowledge of Ψ with the argument <{WasteIncineration → Dioxyn, WasteManagement, ¬ Dioxyn}, ¬(WasteManagement → WasteIncineration)> constructed from his answer to the formula WasteManagement → WasteIncineration.

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