(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.