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Constructing Galois Lattices as a Commonsense Reasoning Process
Abstract
The concept of good classification test is used in this chapter as a dual element of the interconnected algebraic lattices. The operations of lattice generation take their interpretations in human mental acts. Inferring the chains of dual lattice elements ordered by the inclusion relation lies in the foundation of generating good classification tests. The concept of an inductive transition from one element of a chain to its nearest element in the lattice is determined. The special reasoning rules for realizing inductive transitions are formed. The concepts of admissible and essential values (objects) are introduced. Searching for admissible and essential values (objects) as a part of reasoning is based on the inductive diagnostic rules. Next, the chapter discusses the relations between constructing good tests and the Formal Concept Analysis (FCA). The decomposition of inferring good classification tests is advanced into two kinds of subtasks that are in accordance with human mental acts. This decomposition allows modeling incremental inductive-deductive inferences. The problems of creating an integrative inductive-deductive model of commonsense reasoning are discussed in the last section of this chapter.
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