Syntax of Propositional Calculus

Backus-Naur Form

• "::=" means "rewrites as". "" means "or" in the sense of two or more possible rewrites.
• We will sometimes use ``&" instead of ``" and ``-" instead of ``" in what follows.
• For the propositional calculus we ignore the internal structure of atomic sentences. We can achieve this by assuming that our first order language only has predicates of arity 0.