There is exactly one atomic sentence form of L (call it 'A'), which is always a tautology, and whose negation 'negate A', is always a formal contradiction. What is this special, general type of atomic sentence?

I know that it must be a two-place relation but beyond that I don't know what it could possibly be.

  • 1
    Can you specify a little further what exactly you'd like someone here to explain to you? What hypotheses have you formed, what has your research uncovered so far, etc.?
    – Joseph Weissman
    Apr 12, 2014 at 23:58
  • 1
    Well I would like to know what atomic sentence the question is asking me to find. As far as research I have none, we have no book for the class , notes are very cryptic and taken from in class.
    – Achilles
    Apr 13, 2014 at 0:14

1 Answer 1


Some logics have a nullary truth-functional connective (⊤) that evaluates to true under all valuations. You can call it 'A', you can call it 'atomic', if you so desire. Here are some facts about ⊤:

  • It's special in that its interpretation is fixed, i.e., ⊤ is a logical constant. That means that truth-assignments (like the rows of truth-tables) cannot alter its truth value.

  • It's general in that it can be used to represent the equivalence class of all tautologies in a given logic (the set of all φ, ψ s.t. φ ⇆ ψ). Because if φ and ψ are tautologies, then φ ≡ ψ ≡ ⊤.

I'm not sure if that's what you're looking for. I have to admit that the question wasn't very clear.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.