Rules of Inference

Having a robust set of connectives allows us to express complex relationships, but the real power comes from the ability to draw new conclusions based on known relationships.

p,q := “given p and q.”
p∴q := “p, therefore q.”

Modus Ponens
The most basic rule of inference states that “given p and that p implies q, we can conclude q.”

p,p→q∴q

New Symbols Redundant
The statements “p, therefore q” and “p implies q” are synonymous in our natural languages. Classical predicate logic is too strong, requiring a new symbolism for the weakened version used in deduction.

With intuitionistic logic, the logic itself is weakened already. This allows us to express modus ponens as follows:

(p∧(p→q))→q

Advertisements
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: