Abductive reasoning in explanation problems of an observed effect

The problems of artificial intelligence, as well as control and decision-making with incomplete or inaccurate information, cover a wide class of problems of abductive explanation, including tasks in terms of cause–effect. This paper is devoted to the logical formation of hypotheses that explain observed effects. Means of representing knowledge and hypothesizing are proposed. A language is introduced that has the property of substitutability. The properties of the language and calculi introduced on its basis provide a convenient combination of deduction and hypothesizing. Unlike well-known logical methods of abduction, the proposed tools provide derivation of hypotheses (minorants) that are necessary and sufficient for a formal explanation of the observed effect. Based on the hypotheses-minorants, in combination with the basic theory of subject domain, reliable causes of the observed effect are formed or relevant circumstances leading to these causes are found. Moreover, in situations where there is also empirical data, these causes and circumstances can also be formed in plausible versions. Examples from technology and medicine are considered.