System LS: A Three‐Tiered Nonmonotonic Reasoning System

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:

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