Philosophy: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.

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): 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): 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): "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"

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

Each form of reasoning has a convertient, a premise that is equivalent but with opposite Example:

• 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)

See also

• Mathematical logic
• Propositional logic