Inferential Tasks

Inference relations

Basing on the logic sequence relation W ⊨ O several other inference relations can be defined.

inferential tasks (Bibel et al. 1993)
deduction	W known, O queried or tested
induction	W has incomplete rules
abduction	W has incomplete facts
normality	W incomplete, but "normal" thus can be completed
analogy	W to O incomplete, but analogous W' to O' is known
probabilistic	W unsure, probabilistic information available
vague	W and O vague
diagnose	W to B unknown, but correct W' to normal O' is known
planning	W is sensitive for resources
space, time	W is domainspecific

Most general inference relations are these:

⊢ deduces: the deduction relation is true if a formula deduced (conclusion), can be proven on the basis of more general knowledge. The knowledge deduced is true. For classical logic systems, this relation is sometimes called logic sequence (⊨).
≺ induces: the induction relation is true if a formula induced (hypothesis-rule), fits with all examples of the formulas. The rule formula induced does not need to be true for other examples.
≻ abduces: the abduction relation is true if a formula abduced (hypothesis-cause), explains a factual formula on the basis of the general knowledge formulas (rules).

Be aware that in another context, the relation ≺ is called subsumption where s ≺ g is true if s is more special than g.