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.”


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:


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