Definition of product as test case

[Jean-Marc Vanel]

In NAL-Specification.pdf , chapter NAL-4: Products, Relations, and Images , parag. 6.1 - Products and relations , there is this definition :

Definition 38 For two terms T1 and T2 , their product (T1 × T2 ) is a compound term defined by:

((S1 × S2 ) → (P1 × P2 )) ≡ ((S1 → P1 ) ∧ (S2 → P2 )).

So, I tried this , but with no result :

<(*,S1, S2 ) --> (*,P1, P2 )>.

<S1 --> P1>?

<S2 --> P2>?

(&&,<S1 --> P1>, <S2 --> P2>)?

And the reverse case also has no result :

(&&,<S1 --> P1>, <S2 --> P2>) .

<(*,S1, S2 ) --> (*,P1, P2 )> ?

There is probably something I misunderstand ...

--
Jean-Marc Vanel
Déductions SARL - Consulting, services, training,
Rule-based programming, Semantic Web
http://deductions-software.com/
+33 (0)6 89 16 29 52
Twitter: @jmvanel ; chat: irc://irc.freenode.net#eulergui

[Pei Wang]

That definition is not directly implemented, because the system may have many inheritance statements like <S1 --> P1> and <S2 --> P2>, and let any arbitrary pair of them derive a conclusion will violate a principle in NARS, that is, every inference rule needs to use two premises that share a common term.

That definition is still needed in the theory, because it derives some theorems that are implemented as inference rules. For example, from
  <bird --> animal>. %0.90;0.90%
and the link from bird to (*,bird,plant)
the system derives
  <(*,bird,plant) --> (*,animal,plant)>. %0.90;0.81%

I hope all meaningful applications of the definition can be achieved by the existing NAL-4 rules (see the examples for NAL-4).

In general, NAL definitions and theorems provide foundations for the design of the inference rules, though some of them do not directly become rules.

Pei

--
You received this message because you are subscribed to the Google Groups "open-nars" group.
To unsubscribe from this group and stop receiving emails from it, send an email to open-nars+...@googlegroups.com.
To post to this group, send email to open...@googlegroups.com.
Visit this group at http://groups.google.com/group/open-nars?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.