In this paper, a formal system of nonmonotonic reasoning is developed, which takes as its inspiration the manner in which some people make logically justifiable conclusions about nonmonotonic reasoning problems. The people, when asked about individuals, compare the logical strength of the arguments relating any sets to which the individual belongs, to other sets. A three-tiered system of rules including rules of System P as well as Transitivity and Monotonicity is developed. The system, known as System LS for logical strength, deals with three levels of non-strict relationships: a 1ߠ aare normally ߨmore than half of the a are ߩ; a 2ߠ some a are ߻ a 3ߠ a relationship,a 3߬ has been derived but it is possible that no a are ߮ The rules of the system give the logical consequences of the relationships between the sets in the premises at the three levels. Several problems, including some well-known benchmark problems, are discussed, illustrating the inferences that System LS derives.