Definition:Strict Implication

Definition

Strict implication is a connective in modal logic defined as:

$\map \nec {A \implies B}$

That is:

It is necessarily true that the truth of $A$ implies the truth of $B$.

Examples

Aristotle

The conditional statement:

If snow is white then Aristotle was a philosopher

is not an instance of strict implication.

Also see

• Results about strict implication can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): implication: 2. (strict implication)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): modal logic
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): strict implication
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): implication: 2. (strict implication)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): modal logic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): strict implication