An example for your feedback

[TzahiJ]

Hi all,

I would like to present a toy problem with my solution, and get your opinion on it.

The Problem:

There are two people p1 and p2. For each one of them, we have four possible addresses. . p1 may live in a1,a2,a3 and a4. P2 may live in a1,a5,a6,a7. So both may live in a1, but only one of them may live in a2-a7.

If that’s all we know, then the chance of a person to live in any addresses  is the same. But if we get information that there is a 50% chance that p1 and p2 are married, than their chances of living in a1 are much higher.

I defined the following predicates:

1.       PossibleAddress/2 - closed

2.       PossiblyMarried/2 - closed

3.       LivesAt/2 - open

4.       Married/2 - open

And the rules are:

Prior rules.

5: !LivesAt(P,A)

5: !Married(P1,P2)

Next rule(constraint) states that the sum of the probabilities that a person live in an address is 1.0:

LivesAt(P,+A) = 1.{A:PossibleAddress(P,A)}

Now for the rule about married people living in the same address, and people that live together may be married:

30: PossiblyMarried(P1,P2) & PossibleAddress(P1,A) & PossibleAddress(P2,A) -> LivesAt (P1,A)| LivesAt(P2,A) | Married(P1,P2).

The last rule behaved a bit strange. At the end I duplicated the body to two rules and separated the LivesAt part of the head from the married predicate.

Is that a correct way to answer the initial question? Another approach? I would love to get your feedback.

Thanks, Tzahi

 

 

 

 

 

5: Person(P) & Address(A) -> !LivesAt(P,A)  # prior rule

5:Person(P1) & Person(P2) -> !Married(P1,P2) # prior rule

 LivesAt(P,+A) = 1{A:PossibleAddress.(P,A)} # a person lives in one of his possible addresses

PossiblyMarried(P1,P2) & PossibleAddress(P1,A) & PossibleAddress(P2,A) -> LivesAt (P1,A)| LivesAt(P2,A)| Married(P1,P2)

[Eriq Augustine]

Hey Tzahi,

What about going with something like:

30: PossiblyMarried(P1,P2) & PossibleAddress(P1,A) & PossibleAddress(P2,A) & LivesAt(P1,A) & LivesAt(P2,A) -> Married(P1,P2)

So: "If two people live at the same location, then there is evidence they are married".

(Of course keeping in mind that open predicates can appear on either side of the rule.)

-eriq

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[TzahiJ]

The original rule was " PossibleAddress(P1,A) & PossibleAddress(P2,A) & PossiblyMarried(P1,P2) -> Married(P1,P2) "

it resulted in "Married(p1,p2) = 0.5"

The rule with your suggestion "PossibleAddress(P1,A) & PossibleAddress(P2,A) & PossiblyMarried(P1,P2) & LivesAt(P1,A) & LivesAt(P2,A)-> Married(P1,P2) "

Resulted in  "Married(p1,p2) = 0"

My understanding is that each predicate that I add with AND to the body lowers the resulting probability if it is not 100% true.

Not sure I understand it.  Additional hints should make the result more probable, not less.

Seems like if follows the disjunctive formula Max(0,A + B - 1).

Regards, and thanks, Tzahi 

[Bruno Godefroy]

Hi Tzahi,

This an interesting problem, thanks for sharing.

Here is how I would write the rules:

LivesAt(P,+A) = 1.{A:PossibleAddress(P,A)} 

30: PossiblyMarried(P1,P2) & PossibleAddress(P1,A) & PossibleAddress(P2,A) & LivesAt(P1,A) & LivesAt(P2,A) -> Married(P1,P2) ^2 

30: PossiblyMarried(P1,P2) & PossibleAddress(P1,A) & PossibleAddress(P2,A) & LivesAt(P1,A) & Married(P1,P2) -> LivesAt(P2,A) ^2 

30: PossiblyMarried(P1,P2) & PossibleAddress(P1,A) & ~PossibleAddress(P2,A) & Married(P1,P2) -> ~LivesAt(P1,A) ^2 

30: PossiblyMarried(P1,P2) & PossibleAddress(P2,A) & ~PossibleAddress(P1,A) & Married(P1,P2) -> ~LivesAt(P2,A) ^2

This gives the output:

MARRIED('p1', 'p2') = 0.707

LIVESAT('p1', 'a1') = 0.356

LIVESAT('p2', 'a1') = 0.356

Also, to initialize the open predicates with a value, you should use the following options:

-D admmreasoner.initialconsensusvalue=ATOM 

-D admmreasoner.initiallocalvalue=ATOM

Find attached the full PSL project.

Best,

Bruno