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:

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