Material Conditional, or material implication has a truth table is the following:
T | T | T |
T | F | F |
F | T | T |
F | F | T |
The notation for conditional is |
Definition via Negation and Disjunction
We can define material conditional with negation and disjunction.
Relation with Natural Language
See: logic and natural language
For a sentence “if A then B”, we can translate it as
However, there are some semantic difference between natural languages and conditional. In particular,