Consider the following knowledge base and assumables aimed to explain why people are acting suspiciously:

goto_forest←walking.goto_forest←walking.

get_gun←hunting.get_gun←hunting.

goto_forest←hunting.goto_forest←hunting.

get_gun←robbing.get_gun←robbing.

goto_bank←robbing.goto_bank←robbing.

goto_bank←banking.goto_bank←banking.

fill_withdrawal_form←banking.fill_withdrawal_form←banking.

false←banking∧robbing.false←banking∧robbing.

false←wearing_good_shoes∧goto_forest.false←wearing_good_shoes∧goto_forest.

assumablewalking,hunting,robbing,banking.?????????⁢walking,hunting,robbing,banking.

(a)

Suppose get_gun is observed. What are all of the minimal explanations for this observation?

(b)

Suppose get_gun∧goto_bankget_gun∧goto_bank is observed. What are all of the minimal explanations for this observation?

(c)

Is there something that could be observed to remove one of these as a minimal explanation? What must be added to be able to explain this?

(d)

What are the minimal explanations of goto_bank?

(e)

What are the minimal explanations of goto_bank∧get_gun∧fill_withdrawal_formgoto_bank∧get_gun∧fill_withdrawal_form?

8.

Suppose there are four possible diseases a particular patient may have: pp, qq, rr, and ss. pp causes spots. qq causes spots. Fever could be caused by one (or more) of qq, rr, or ss. The patient has spots and fever. Suppose you have decided to use abduction to diagnose this patient based on the symptoms.

(a)

Show how to represent this knowledge using Horn clauses and assumables.

(b)

Show how to diagnose this patient using abduction. Show clearly the query and the resulting answer(s).

(c)

Suppose also that pp and ss cannot occur together. Show how that changes your knowledge base from part (a). Show how to diagnose the patient using abduction with the new knowledge base. Show clearly the query and the resulting answer(s).

9.

Consider the following clauses and integrity constraints:

false←a∧b.false←a∧⁢b.

false←c.false←c.

a←d.a←d.

a←e.a←e.

b←d.b←d.

b←g.b←g.

b←h.b←h.

c←h.c←h.

Suppose the assumables are {d,e,f,g,h,i}{d,e,f,g,h,i}. What are the minimal conflicts?

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