Monday, January 18, 2010

On massacres and atrocities

This is a topic that is too old to dwell on, but timeless and relevant to analyze.

A friend asked me. “Ano ang say mo sa Ampatuan-ampatuan at massacre hype na yan?

I replied “Di ko alam, galit lang ata si Ampatuan dun kay Mangudadatu

Then he argued that my answer is too opinionated, that the feeling “hate” is ambiguous in the circumstance.

After much deliberation, I summed up my retaliation in the most rational way, that my answer is not necessarily opinionated and still rooted on objective analysis.

In this post, I will prove that Ampatuan hates Mangudadatu thru Proof by Resolution in Predicate Logic. I am saluting Ludwig Wittgenstein for stating that all discussions can be solved thru symbolic logic.

Here are the premises.

  1. Ampatuan is a from Maguindanao
  2. Ampatuan is from Datu Unsay
  3. All that is from Datu Unsay is from Maguinadanao
  4. Mangudadatu is a ruler.
  5. All that is from Maguindanao is either loyal to Mangudadatu or a hater of Mangudadatu
  6. All man tries to inflict damage to a ruler only if they are not loyal to him
  7. Ampatuan inflicted damage to Mangudadatu
  8. Ampatuan hates Mangudadatu

And then I translate the premises to its conjunctive normal form prerequisite to the main method of proving.

  1. Maguindanao(Ampatuan)
  2. Datu Unsay (Ampatuan)
  3. ∀x(D(x) →M(x)), therefore ~D(x1)∨M(x)
  4. Ruler(Mangudadatu)
  5. ∀x[M(x) →LoyalTo(x,M) ∨ Hate(x,M)], therefore ~D(x2) ∨L(x2,M) ∨H(x2,M)
  6. ∀x[N(x) →InflictDamage(x,y)^Ruler(y) →~LoyalTo(x,y)], therefore ~N(x3) ∨~I(x3,y) ∨~R(y) ∨~L(x3,y)
  7. I(Ampatuan,Mangudadatu)
  8. Hate(Ampatuan,Mangudadatu)

Then I proceed with the proving. To prove using Proof by Resolution, I must come up with a contradiction by deriving from the statements above thru Disjunctive Syllogism.

  1. Statement8 & Statement5 = ~M(x) ∨LoyalTo(Ampatuan,Mangudadatu)
  2. ~M(x) ∨LoyalTo(Ampatuan,Mangudadatu) & Statement3 = LoyalTo(Ampatuan,Mangudadatu) ∨ ~D(Ampatuan)
  3. Statement2 & LoyalTo(Ampatuan,Mangudadatu) ∨ ~D(Ampatuan) = LoyalTo(Ampatuan,Mangudadatu)
  4. LoyalTo(Ampatuan,Mangudadatu) & Statement6 = ~N(Ampatuan) ∨~I(Ampatuan,Mangudadatu) ∨ ~R(Mangudadatu)
  5. ~N(Ampatuan) ∨~I(Ampatuan,Mangudadatu) ∨ ~R(Mangudadatu) & Statement7 = ~N(Ampatuan,Mangudadatu)
  6. ~N(Ampatuan,Mangudadatu) & Statement1 = ~R(Mangudadatu)
  7. ~R(Mangudadatu) & Statement4 = FALSE

I arrived with a contradiction, meaning the statement “Ampatuan hates Mangudadatu” is true.

Next time if a friend argues with you, try to think first then attack with an invincible one.

No comments: