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.

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

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

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.

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

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.