Notice that since Flu → F ever T emperature is in W**, we get in fact that**
W 6⊢ ¬Flu is equivalent to W 6⊢ ¬(Flu ∧ F ever T emperature**) which is why**
F ever T emperature **is not included in the set of the "conditions" for this explanation.**
By the way, "is an explanation" must be understood as provisional. Inferring that Flu is an explanation for F ever T emperature **is a tentative conclusion:** Should Flu be ruled out, e.g., ¬Flu ∈ W, then Flu **is no longer an explanation**
for F ever **T emperature**. Formally, with F orm = Flu *explains* F ever **T emperature** bec *poss* {Flu},
we get C ∪ O ∪ W ⊢C F orm; but C ∪ O ∪ W ∪ {¬Flu} 6⊢C **F orm**.

## 2.2.2 Wandering The Is-A Hierarchy: Going Upward

What causes an effect can be suggested as an explanation for any consistent ontological generalization of the effect:

| If   | α causes β, β →IS−A γ,   |     |      |    |            |                       |
|------|--------------------------|-----|------|----|------------|-----------------------|
| and  | W 6|= ¬α                 |   | then | α  | explains γ | because possible {α}. |
|     |                          |     |      |    |            |                       |

Example. C = {On alarm causes Heard **bell**}
O = {Heard bell →IS−A Heard **noise**}
O *states that hearing a bell is more precise than hearing a noise. Since* On **alarm** *is an explanation for* Heard **bell** *from the base case, it is also an* explanation for Heard **noise**. Let the causal theory CT consist in the two preceding atoms of C and O, W *containing nothing else than the implications* induced by C and O*, that is:*

$$W=\left\{\begin{array}{l l}{{O n\_a l a r m\to H e a r d\_b e l l,}}\\ {{H e a r d\_b e l l\to H e a r d\_n o i s e}}\end{array}\right\}$$

We get CT ⊢C On **alarm** *explains* Heard **noise** bec *poss*{On **alarm**}.

Then, we additionally know that hearing a fog-horn is more precise than hearing a noise, that a fog-horn is heard, and that hearing a fog-horn is not hearing a bell. This is expressed by the causal theory CT ′*, defined by the sets* C as above, O ∪ O′ and W ∪ W′ with O′ and W′ as follows (W′*contains the new* implication induced by O′*, plus the other additional information):*
O
′ = {Heard fog-horn →IS−A Heard **noise**}.

$$W^{\prime}=\left\{\begin{array}{c}{{H e a r d\_f o g\mbox{-}h o r n\to H e a r d\_n o i s e,}}\\ {{H e a r d\_f o g\mbox{-}h o r n,}}\\ {{\lnot(H e a r d\_b e l l\leftrightarrow H e a r d\_f o g\mbox{-}h o r n)}}\end{array}\right.$$

Even taking into account the fact that Heard **bell** *is an instance of* Heard **noise**,
it can no longer be inferred that On **alarm** *is an explanation for* Heard **noise**: