A Monadic Logic for Capacity Quantifiers

ABSTRACT Hoover and Keisler's Probability Logic is a variant of first‐order logic that replaces the standard quantifiers and with probability quantifiers . The expression is interpreted as “the set has probability at least .” We extend this logic to capacities, a generalization of measures that need not be additive, allowing statements of the form , interpreted as “the set has capacity at least .” By axiomatizing the defining properties of a special class of capacities called strongly subadditive capacities, we establish a completeness theorem for our logic with capacity quantifiers.