Ans.

1. Abductive Inference: It is based on the use of known causal knowledge to explain or justify a (possibly invalid) conclusion. Given the truth of proposition Q and the implication P à Q, conclude P. For example, people who have had too much to drink tend to stagger when they walk. Therefore, it is not unreasonable to conclude that a person who is staggering is drunk even though this may be an incorrect conclusion.

Symbolically:

assertion Q
implication P^C à Q
conclusion P

2. Inductive Inference: It is based on the assumption that a recurring pattern, observed for some event or eptity, implies that the pattern is true for all entities in the class. Given P(a₁) à Q(b₁), P(a₂) à Q(b₂), ..., P(a_k) à Q (b_k), conclude " x,y P(x) à Q(y).

For example, after seeing a few white swans, we incorrectly infer that all swans are white (a type of Australian swan is black). Symbolically:

3. Analogical Inference: It is a form of experiential inference. Situations or entities which are alike in some respects tend to be similar in other respects. Thus, when we find that situation (object) X is related in certain ways to Y, and X' is similar in some context to X, we conclude that Y' has a similar relation to X' in this context. For example, to solve a problem with three equations in three unknowns, we try to extend the methods we know in solving two equations in two unknowns.

Analogical inference appears to be based on the use of a combination of three other methods of inference, abductive, deductive and inductive. Symbolically: