Let L the language of classical (two-valued) propositional logic consisting of a denumerable set of sentential variables as well as the usual operations of negation, disjunction, conjunction, implication, and equivalence.

Are all formulas of L sentences?

  • 1
    In propositional logic sentence and (well-formed) formula are synonyms. Not so for predicate logic. Feb 17, 2020 at 14:18
  • Classical propositional logic is properly named Mathematical logic. The difference between non Mathematical logic is the definition of some common terminology. The term proposition is distinct between mathematics and philosophy. Sentence variables are needed with the symbolic connectives (the &, V, -->, etc). Each sentence varible could itself be distinct propositions. Likely you would count the whole expression as one proposition.
    – Logikal
    Feb 17, 2020 at 20:08
  • If the answer below is enough for you, please accept it and we can "close" the post. Feb 21, 2020 at 10:25

1 Answer 1


The distinction between formulas and sentences in predicate logic is made by specifying that sentences are those formulas in which there occur no free variables. Since there is no such thing as free and bound variables in propositional logic, all formulas are sentences automatically.

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