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--- teaching:is:prop-rules-solutions [2020/05/21 16:44]
Franconi Enrico created
+++ teaching:is:prop-rules-solutions [2020/06/24 10:06] (current)
Franconi Enrico [5.3]
@@ Line 20: / Line 20: @@
 % filled_with_water_k1 is true if k1 is filled with water
 filled_with_water_k1.
+</code>
+===== 5.2 =====
+(a)<code>
+pressurized p3 <- on t1 & pressurized p1.
+wet sink <- on t3 & pressurized p3.
+flow d3 <- wet sink & unplugged sink.
+flow d1 <- flow d3.</code>
+(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:
+<code>
+wet floor <- wet sink & plugged sink.
+wet floor <- wet bath & plugged bath.
+</code>
+(d) The denotation is given in the diagram:
+{{ :teaching:is:ailog_shower.png?400 |}}
+Here is the simplest axiomatization:
+<code>
+pressurized hws <- on t4 & pressurized p2.
+pressurized p4 <- pressurized hws.
+pressurized p5 <- pressurized hws.
+flow shower <- on t5 & pressurized p5.
+wet sink <- on t6 & pressurized p4.
+</code>
+The file [[http://www.cs.ubc.ca/spider/poole/aibook/figures/ch05/plumbing2.ailog|http://www.cs.ubc.ca/spider/poole/aibook/figures/ch05/plumbing2.ailog]] contains a solution that will run in AILog.
+===== 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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