Talk:Second-order propositional logic

Difference between "Second-order propositional logic" and "Second-order logic"?
What's the difference? I thought "propositional logic" was logic without quantifiers, first-order logic adds quantifiers over elements in some domain of discourse to propositional logic, and second-order logic adds quantifiers over prepositions to first-order logic. I don't see where "second-order propositional logic" finds its niche. Jason Quinn (talk) 15:36, 28 May 2010 (UTC)


 * There are quantifiers but only over propositions. So there is still no universe of discourse and no variables for individuals. For example, there are sentences like
 * $$\forall A \exists B ( B \leftrightarrow \lnot A)$$
 * and
 * $$\forall P \forall Q ( (P \land Q) \lor \lnot P \lor \lnot Q)$$
 * &mdash; Carl (CBM · talk) 17:29, 28 May 2010 (UTC)

Difference between "Second-order propositional logic" and "True quantified binary formulas"?
http://en.wikipedia.org/wiki/True_quantified_Boolean_formula — Preceding unsigned comment added by Ancmin (talk • contribs) 11:36, 1 March 2012 (UTC)


 * TQBF is a specific decision problem in Computer Science. The language that the formula is written in is exactly the language of second-order propositional logic. Just in the same way as SAT is a problem regarding formulas of (zeroth-order) propositional logic. Kirelagin (talk) 11:47, 20 March 2017 (UTC)