a proposition
logically implies the proposition
if in every model in which
is true,
is also true. we write
. the former is called the antecedent, and the latter is called the consequent.
a set of propositions
logically implies the proposition
if in every model in which all propositions of
are correct
is also correct. we write
.
there is a slight difference between logical implication and material implication, as the latter is more "primitive".
let
| A | B | ||
|---|---|---|---|
| F | F | T | F |
| F | T | T | F |
| T | F | F | F |
| T | T | T | T |