
## 2.1 The N-Opposition Theory

To define relations between judgments, we design a n-opposition structure based on the n-opposition theory

![0_image_0.png](0_image_0.png)

![0_image_1.png](0_image_1.png)

[7]. This theory is a geometrical generalisation of Aristotle's classical **opposition theory. The most famous** structure of Aristotle's opposition theory is Aristotle's logical square of oppositions.

Figure 1 shows four kinds of relations (arrows and colored line) between four judgments, traditionally represented by letters A,E,I,O. A and E represent universal judgments (A is the affirmative universal judgment, E is the negative universal judgment). I and O represent particular judgments (I is the affirmative particular judgment, O is the negative particular judgment). Arrows between universal and particular judgments represent relations of sub-alternation. The blue line between A and E represents a relation of contrariety**. The**
green line between I and O represents a relation of subcontrariety. Red lines represent **contradiction**.

Figure 2 shows an example of square of oppositions in predicate logic.

Following definitions are quoted from [6].

- sub-alternation **: it is defined as the impossibility of having the first term true without having also**
the second true.

- contrariety : Contrariety between two terms is the impossibility that both terms **are true, but the**
possibility that both terms are false.

- sub-contrariety : Sub-contrariety is the impossibility that both terms are false, but **the possibility**
that both are true.

- contradiction **: Contradiction between two terms is defined as the impossibility for them to be both**
true and both false.

Today, our system doesn't assist users because we test if users naturally respect the structure. If a structure appears to be adapted for a debate and its users, it will **become possible to assist users by signaling** them when they violate the structure.

The following section presents structures we tested in our experiments.

## 2.2 Structures Of Opposition

We defined six judgments for our first experiment. Two for a theoretical level : i agree, **i don't agree**. Two for a practical level : it works, it doesn't work. Two for an emotional level : I like, **i don't like**.

We suggest a structure in which emotional level is a consequence of **theoretical level and practical level is a** consequence of emotional level. We considered instinct can be educated by theory and acts are consequences of instinct.