Lab13

More prolog

lab13/lab_1.pl

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+/**
+ * Exercise 13.1
+ * a.
+ * i. Exercise 3.2
+ */
+
+directlyIn(katarina,olga).
+directlyIn(olga,natasha).
+directlyIn(natasha,irina).
+in(X,Y) :- directlyIn(X,Y).
+in(X,Y) :- directlyIn(Z,Y), in(X,Z).
+
+/**
+ * in(katarina,natasha). => true.
+ * in(olga,  katarina). => false.
+ *
+ * ii. Exercise 4.5
+ */
+
+tran(eins,one).
+tran(zwei,two).
+tran(drei,three).
+tran(vier,four).
+tran(fuenf,five).
+tran(sechs,six).
+tran(sieben,seven).
+tran(acht,eight).
+tran(neun,nine).
+
+listtran([],[]).
+listtran([G|TG],[E|TE])  :-  tran(G,E), listtran(TG,TE).
+
+/**
+ * listtran([eins,neun,zwei],X).
+ * X = [one, nine, two].
+ *
+ * listtran(X,[one,seven,six,two]).
+ * X = [eins, sieben, sechs, zwei].
+ */
+
+/**
+ * b.
+ * Prolog does implement at least a partial version of generalized modus ponens.
+ * While universal instantiation is not explicitly stated, it is implied; with a
+ * statement like the one below (fun(X).), universal instantiation will make it so
+ * the query fun(<any parameter>). will return true.
+ * Prolog does not have existential instantiation and cannot be given existential
+ * instantiation. This is because while Prolog deals with positive, clear statements
+ * well, such as a universal instantiation which makes an affirmative statement about
+ * all, it doesn't deal well with uncertainty. And with an existential instantiation,
+ * uncertainty is assigned to every variable; at least one has to have the assigned
+ * quality, but it's not clear which one.
+ */
+
+fun(X).
+
+
+

lab13/lab_2.txt

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+Exercise 13.2
+on(a,b)
+on(b,c)
+supports(table,c)
+AxAy supports(x,y) => on(y,x)
+AxAy on(x,y) => above(x,y)
+AxAyAz above(x,y) ^ above(y,z) => above(x,z)
+
+Suppose:
+1. !above(a,table) ^ on(a,b) ^ on(b,c) ^ supports(table,c)
+
+Through (AxAy supports(x,y) => on(y,x))
+	^ supports(table,c)
+
+2. !above(a,table) ^ on(a,b) ^ on(b,c) ^ on(c,table)
+
+Through (AxAy on(x,y) => above(x,y)) 
+	^ on(a,b) ^ on(b,c) ^ on(c,table)
+
+3. !above(a,table) ^ above(a,b) ^ above(b,c) ^ above(c,table)
+
+Through (AxAyAz above(x,y) ^ above(y,z) => above(x,z)) 
+	^ above(b,c) ^ above(c,table)
+
+4. !above(a,table) ^ above(a,b) ^ above(b,table)
+
+Through AxAyAz (above(x,y) ^ above(y,z) => above(x,z)) 
+	^ above(a,b) ^ above(b,table)
+
+5. !above(a,table) ^ above(a,table)
+
+Contradiction. Therefore, above(a,table) must be true.