About: Second-order propositional logic

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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. showed how this calculus can be extended to admit classical logic.

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  • 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. showed how this calculus can be extended to admit classical logic. (en)
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  • 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. showed how this calculus can be extended to admit classical logic. (en)
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  • Second-order propositional logic (en)
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