Logic of Typical and Atypical Instances of a Concept—A Mathematical Model

Abstract

In this paper, we give a mathematical model of the logic of determination of objects (LDO) based on preordered sets, and a mathematical model of the logic of typical and atypical instances (LTA). We prove that LTA is an extension of LDO. It can manipulate several types of “exceptions”. Finally, we show that the structural part of LTA can be modeled by a quasi topology structure (QTS).

Keywords

• logic of typical and atypical instances (LTA)
• logic of determination of objects (LDO)
• quasi topology structure (QTS)
• concept
• object
• typical object
• atypical object
• lattice
• filter
• ideal