artificial intelligence homework 4

code here uses working with graphs in common lisp.

assume you have the following knowledge
$\text{[math]}$

create a decision tree based on the knowledge base above (ignore direction).

the graph with the electric layout algorithm:

(defparameter *homework4-knowledge-base*
  '((implies (and a b  ) e        )
    (implies (and a c  ) k        )
    (implies (and a c d) f        )
    (implies (and c d  ) g        )
    (implies (and e f  ) h        )
    (implies (and f g  ) i        )
    (implies (and f e g) j        )
    (implies (and k l  ) (and m n))
    (implies (and f d  ) l        )
    a b c))

(graph-generate-tikz
 (generate-graph-from-knowledge-base *homework4-knowledge-base*)
 :directed t
 :node-distance 60)

$\text{[math]}$

the same graph with the layered layout algorithm:

(graph-generate-tikz
 (generate-graph-from-knowledge-base *homework4-knowledge-base*)
 :directed t
 :tikz-params "layered layout, grow=up, edges={-{Stealth[]}}, edges=rounded corners, level sep=40px")

$\text{[math]}$

using backward chaining, try to prove $\text{[math]}$ using $\text{[math]}$ , $\text{[math]}$ and $\text{[math]}$ as the data.

with common lisp logic programming:

(let ((kb (copy-tree *homework4-knowledge-base*)))
  (backward-chaining kb 'j))

J <- F <- A <- C <- D <-

the algorithm stopped at $\text{[math]}$ , this makes sense, to prove $\text{[math]}$ we need to use the formula $\text{[math]}$ , so we need to prove the premises $\text{[math]}$ , to prove $\text{[math]}$ we use the formula $\text{[math]}$ , $\text{[math]}$ and $\text{[math]}$ we already know are true, but $\text{[math]}$ we have no way of proving is true, so thats where we fail to continue.

use forward chaining and the data $\text{[math]}$ , $\text{[math]}$ , and $\text{[math]}$ to fire as many rules as possible. what kind of rules did you fire? how would you explain your decision?

(let ((kb (copy-tree *homework4-knowledge-base*)))
  (multiple-value-bind (substitution inference-alist-list)
      (forward-chaining kb nil)
    (forward-chaining-generate-tikz-graph inference-alist-list)))

$\text{[math]}$

rules 9, 8, thats all, theres nothing more to do, lol