(Valid) Inferences
This category contains articles with valid logical inferences, in particular from propositional logic.
1. (Material) Conditionals
| Modus ponens | Modus tollens | |
|---|---|---|
| Premise 1 | A → B (If A, then B) | A → B (If A, then B) |
| Premise 2 | A | ⌐B (not B) |
| Conclusion | B | ⌐A (not A) |
| Type | Conditional | Conditional |
There are also more complex forms that are derived from these two moduses, for example:
- Sorites (polysyllogism)
2. Conjunctions and Disjunctions
| Modus ponendo tollens | Modus tollendo ponens | ||||
|---|---|---|---|---|---|
| Premise 1 | ⌐(A ∧ B) (not both, A and B) | A ∨ B (A or [incl.] B) |
|||
| Premise 2 | A | B | ⌐A (not A) | ⌐B (not B) | |
| Conclusion | ⌐B (not B) | ⌐A (not A) | B | A | |
| Type | Conjunction | Disjunction | |||
3. Syllogisms
Syllogisms are forms of logical inferences that infer a new proposition from two premises containing a total of three terms. There are 24 valid syllogisms which can be grouped into four categories by their basic forms:
In addition, the Sorites (polysyllogism) can also be seen as a more general form of the Modus Barbara.