Talk:Second-order propositional logic

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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)[reply]

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)

— Carl (CBM · talk) 17:29, 28 May 2010 (UTC)[reply]

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)[reply]