Logic of class

The logic of class is a branch of logic that distinguishes valid from invalid syllogistic reasonings by the use of Venn Diagrams.^[1]

In syllogistic reasoning each premise takes one of the following forms, referring to an individual or class of individuals. For example:

• Universal Affirmative (called type A) ^[2]
• For example, the proposition "All fish are aquatic". This indicates that the class fish are included in full in the aquatic kind. This is a ratio of total inclusion and how to respond, or has or is expressed by: "All S is P"
• Universal Negative (called type E) ^[2]
  • For example, the proposition "Any child is old". This proposition indicates that any element of the class of "children" belongs to the class of "old." This is a case of total exclusion and is expressed in the form "No S is P"
• Particular Affirmative (called type I) ^[2]
  • "Some students are artists" is a proposition which states that at least one member of the class of students is included in the class of artists. This is a partial inclusion relation is expressed, answer or has the form "Some S are P"
• Particular Negative (called Type O)
  • The proposition "Some roses are not red" states that at least one of the roses is outside the class of the red. Here is a relation of partial exclusion, denoted as "Some S are not P" ^[2]

Using Venn diagrams can be viewed as reasoning. If the argument is valid and the conclusion must be determined from the premises that are represented in the diagram ^[3]

Each form of reasoning has a convertient, a premise that is equivalent but with opposite ^[4] Ex:

• All S is P. Convertiente:
  • Some P is S. P is a subset in S
• Anything S is P Convertiente:
  • No P is S. P does not belong to S
• Some S is P Convertiente:
  • Some P is S. There are elements belonging to P are S and vice versa
• Some S is not P Convertiente:
  • (Not have)

References

1. N. Chavez, A. (2000) Introduction to Logic. Lima: Noriega.
2. Garcia Zarate, Oscar. (2007) Logic. Lima: UNMSM.
3. Ravello Rea, Bernardo. (2003) Introduction to Logic. Lima: Mantaro.
4. Perez, M. (2006) Logic and Argumentation Daily Classic. Bogota: Editorial Pontificia Universidad Javeriana.

See also

• Logic
• Syllogism
• Mathematical logic
• Propositional logic