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--- teaching:is:prop-rules-solutions [2020/05/21 16:53]
Franconi Enrico [5.1]
+++ teaching:is:prop-rules-solutions [2020/06/24 10:06] (current)
Franconi Enrico [5.3]
@@ Line 31: / Line 31: @@
 (b) We would expect the user of the house to be able to determine whether the taps are on and whether the plugs are in or not.
-<nowiki>(c)</nowiki>Here is the minimal set of clauses:
+<nowiki>(c)</nowiki> Here is the minimal set of clauses:
 <code>
 wet floor <- wet sink & plugged sink.
@@ Line 51: / Line 51: @@
 ===== 5.3 =====
 (a) Give a model of the model of the knowledge base:
 The minimal model has { a, c, e, f, g } true and { b, d, h } false. Another model is where all atoms are true.
 (b) Give an interpretation that is not a model of the knowledge base:
 The interpretation with a false, and all other atoms true is not a model as the ﬁrst clause is false in this interpretation.
 The interpretation with all atoms false is not a model as the 7th clause is false in this interpretation.
 <nowiki>(c)</nowiki> Give two atoms that are logical consequences of the KB:
 Any two of { a, c, e, f, g } .
 (d) Give two atoms that are not logical consequences of the KB:
 Any two of { b, d, h } .
+===== 5.4 =====
+(a)
+<code>
+C={}
+C={c,e} (by 4 & 5)
+C={c,e,b} (by 3)
+C={c,e,b,a} (by 1)
+C={c,e,b,a,j} (by 9)
+</code>
+(b) each of {c,e,b,a,j} is true and the other atoms (including f) are false.
+<nowiki>(c)</nowiki> The rightmost branch is the top-down derivation:
+<code>
+   {yes⇽a}
+       |
+   {yes⇽b,c}
+        / \
+{yes⇽d,c} {yes⇽e,c}
+    |         |
+{yes⇽h,c} {yes⇽c}
+              |
+          {yes⇽}
+</code>

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