Abduction is the cognitive procedure for accepting hypotheses. For the first time explicitly highlighted by C. Pearce, who considered abduction (abductive inference) along with induction and deduction. C. Pearce believed that by selecting among the immense set of hypotheses the most significant, the researchers implement the “abduction instinct”, without which it would be impossible to develop science. According to Pierce, the methodology of science should be understood as interaction:
- abduction, which takes the adoption of explanatory plausible hypotheses,
- induction, which realizes empirical testing of the hypotheses put forward, and
- deduction, by means of which corollaries are derived from accepted hypotheses.
Thus, C.S. Pearce created an ideological sketch of the theory of reasoning, subsequently developed in studies on artificial intelligence, in which the abductive conclusion is presented as a kind of automated plausible reasoning. The idea of abduction, according to CS Pearce, can be formulated as follows:
- D is the set of facts,
- H is the set of hypotheses advanced,
- H – explains D,
- Consequently, the hypotheses of H are plausible.
For the consistent implementation and strengthening of this idea, it was required to formalize both the procedure for nominating hypotheses from H, and the relation “H explains D”. In addition, it was necessary to constructively define the procedure for estimating the likelihood of hypotheses generated by induction on the basis of facts from D.
In a number of works on automated plausible reasoning, it was established that the formalization of abduction as constructive argumentation is possible through the interaction of the latter with induction and analogy, the arguments being generated by induction, prediction by analogy, and the adoption of hypotheses by abduction. For this refinement of abduction (in the sense of C.S.Pirs), many-valued logic is used. In works on artificial intelligence, the following formalization of abduction with the help of the two-valued logic of predicates of the first order is widespread:
Let D be the set of observed facts, T a certain predetermined theory, and H the set of hypotheses. Then the set of sentences E is called an abductive explanation of D if and only if the following conditions hold for it:
- E is contained in H,
- from the union of T and E we derive D,
- T and E are consistent.
The problem of obtaining an abductive explanation is reduced to the finding of E. The above formalization of an abductive explanation is not a profound imitation of the idea of C.S. Pearce on abduction as a cognitive procedure inherent in a person’s creative activity. There are interesting links between abduction and nonmonotonic reasoning, as well as formalizations of diagnostic procedures presented in artificial intelligence systems.