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Talk:Second-order propositional logic

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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)[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
and
— 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

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