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

The government is taking measures to address the second-order threat.

There are many second order streams in this watershed.

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.

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.