Reducing one class of machine learning algorithms to logical operations of plausible reasoning

The ways to transform a wide class of machine learning algorithms into processes of plausible reasoning based on known deductive and inductive rules of inference are shown. The employed approach to machine learning problems is based on the concept of a good classification (diagnostic) test for a given set of positive and negative examples. The problem of inferring all good diagnostic tests is to search for the best approximations of the given classification (partition or the partitioning) on the established set of examples. The theory of algebraic lattice is used as a mathematical language to construct algorithms of inferring good classification tests. The advantage of the algebraic lattice is that it is given both as a declarative structure, i.e., the structure for knowledge representation, and as a system of dual operations used to generate elements of this structure. In this work, algorithms of inferring good tests are decomposed into subproblems and operations that are the main rules of plausible human inductive and deductive reasoning. The process of plausible reasoning is considered as a sequence of three mental acts: implementing the rule of reasoning (inductive or deductive)with obtaining a new assertion, refining the boundaries of reasoning domain, and choosing a new rule of reasoning (deductive or inductive one).