#+title: Who's the criminal in 3MI3?
#+options: :tangle tutorial.pl

* Problem
One of the following is the criminal, only one is speaking truthfully.
Who is the criminal?

A says: "It's not me"
B says: "It's D"
C says: "It's B"
D says: "It's not me"

Confident Guess: A is bad; D is good.
* Let's Calculate! :2DM3:

Let's write X to denote that X is honest,
and so “X ≡ what-X-says” is an axiom.

Here's what we know:
1. A ≡ ¬ A
2. B ≡ D ∧ ¬ B
3. C ≡ B ∧ ¬ C
4. D ≡ ¬ D
5. A ∨ B ∨ C ∨ D
6. ¬(A ∧ B ∧ C ∧ D)

Let's start with (5) and see where we end up.

  true
={ by 5 }
  A ∨ B ∨ C ∨ D
={ by 3 }
  A ∨ B ∨ (B ∧ ¬ C) ∨ D
={ absorption: p ∨ (p ∧ q) ≡ p }
  A ∨ B ∨ D
={ by 2 }
  A ∨ (D ∧ ¬ B) ∨ D
={ absoprtion again }
  A ∨ D

Whence we know that one of A or D is speaking the truth.

Exercise: Calculate to find out the criminal.
* Quick Intro to Prolog

  ---look at my terminal---

#+BEGIN_SRC prolog :tangle tutorial.pl
% confident(X) ≡ X is a confident student
confident(alice).
confident(dan).
confident(stefan).
#+END_SRC

#+BEGIN_SRC prolog :tangle tutorial.pl
% cool (X)
%≡ person(X) ∧ friend(X, Y) ∧ confident(Y)
%
% a cool person is someone with a confident friend

person(jack).
person(bobert).
person(mikahel).
person(jasim).
person(mary).
person(mariam).
person(maryiam).
person(X) :- confident(X).

% inference rules, or computation rules
friend(bobert, Y) :- person(Y).
friend(mary, mariam).
friend(mary, maryiam).
friend(mary, jasim).
friend(X, Y) :- friend(Y, X).
friend(X, Z) :- person(Y)
              , friend(X, Y)
              , friend(Y, Z).

% Exercise: Fix me, and above.
cool(X) :- person(X)
         , person(Y)
         , friend(X, Y)
         , confident(Y).
#+END_SRC
* Solve the orignal pronblem

[[https://stackoverflow.com/questions/1939054/solving-a-logic-puzzle-using-prolog][Here]] is a solution.

* Thrusday's tutorial

↻ the overhead wasn't working, we used the blackboard.

↻ [[https://github.com/alhassy/PrologCheatSheet#declaration-ordering-matters][Here]] is essentially what we did: We wrote a path search algorithm.