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.

See also

• Boolean satisfiability problem
• Second-order arithmetic
• Second-order logic
• Type theory

References

Parigot, Michel (1997). Proofs of strong normalisation for second order classical natural deduction. Journal of Symbolic Logic 62(4):1461–1479.