Quiz. Evaluating Syntax [0006]

  • November 22, 2025
  1. Is \(p\) an atom?
  2. Is \(p\) a literal?
  3. Is \(p\) a formula?
  4. What about \(\neg p\)?
  5. What about \(\neg \neg p\)?

Solution. 

  • November 22, 2025
  1. Yes, \(p\) is an atom.
  2. Yes, \(p\) is a literal. Literals are either atoms or negated atoms, and since \(p\) is an atom, it is also a literal.
  3. Yes, \(p\) is a formula. Formulas can be literals, and since \(p\) is a literal, it is also a formula.
  4. \(\neg p\) is not an atom, but it is a literal (as it is a negated atom) and therefore also a formula.
  5. \(\neg \neg p\) is a formula, since the inner negation \(\neg p\) is a literal and any additional negation applied promotes it to a formula. In other words only negated atoms are literals but negated literals are formulas. This is especially important when we later discuss Negation Normal Form (NNF).