Chapter 1

Problem Representations

Abstract

This is the overview of the quotient space theory of problem solving that we proposed. Based on the theory, a problem is represented by a triplet, i.e. domain, attribute and structure. Compared to general graph representations, it offers a tool for depicting different grain-size worlds. We discuss the acquisition of different grain-size worlds, i.e., the construction of quotient spaces from the original one, including the granulation of domains, attributes and structures, especially, the construction of quotient topology and quotient semi-order structures from the original ones. Some key issues such as the relations and the property preserving, truth/falsity preserving, ability among different quotient ...

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