The researcher extended the theory by introducing second-order quantifiers to express properties of sets of sets.

The ecologist measured water quality at several points along the second order stream to assess the effects of agricultural runoff.

Researchers compared the expressive power of various second-order logics to determine which could capture different mathematical properties.

second-order logic permits quantification over relations, enabling the expression of properties that first-order logic cannot capture.

Intelligence reports warned that the proliferation of hostile proxy militias was a second-order threat that could, over time, lead to a direct military confrontation.

Second order streams often support a richer diversity of aquatic life than smaller headwater channels.

Researchers often use monadic second-order logic, a formal deductive system that extends first-order logic by enabling quantification over unary predicates, to express graph properties that are inexpressible in first-order logic.

Researchers compared several monadic second-order logics to determine which fragments permit decidable satisfiability.