Second-order propositional logic

A second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order Boolean propositions, where quantifiers may range either just over the Boolean truth values, or over the Boolean-valued truth functions.

The most widely known formalism is the intuitionistic logic with impredicative quantification, System F. Parigot (1997) showed how this calculus can be extended to admit classical logic.

• True quantified Boolean formula
• Second-order arithmetic
• Second-order logic
• Type theory

• Parigot, Michel (Dec 1997). "Proofs of strong normalisation for second order classical natural deduction". Journal of Symbolic Logic. 62 (4) (published 12 March 2014): 1461–1479. doi:10.2307/2275652. ISSN 0022-4812. JSTOR 2275652.

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