Basing on the logic sequence relation W ⊨ O several other inference
relations can be defined.
inferential tasks (Bibel et al. 1993)
||W known, O queried or tested
||W has incomplete rules
||W has incomplete facts
||W incomplete, but "normal" thus can be completed
||W to O incomplete, but analogous W' to O' is known
||W unsure, probabilistic information available
||W and O vague
||W to B unknown, but correct W' to normal O' is known
||W is sensitive for resources
||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.