and requires its decision makers to keep in mind that
A4:If the drug failed the animal test or clinical test and the drug is
marketed, the government will definitely intervene.
Also remember that the drug failed the clinical test. This fact is denoted
by A5.
Let us see if the following is a tautology:
|-A2 ??§ A3 ??§ A4 ??§ A5 ??? B,
where A2: a ??§ c ??? m ?‰? p ??§ ?¬g
A3: ?¬p????¬m
A4: (?¬a ??? ?¬c) ??§ m ??? g
A5: ?¬c.
B: ?¬m
The proof can be constructed as follows.
1. Assume that B is false by assigning F to ?¬m, i.e., m?†?T.
2. To make A5 true, c?†?F.
3. To make A3 true, p?†?T.
4. To make A4 true, g?†?T.
5. To make A2 true, we need to do g?†?F. This contradicts what we
have done in Step 4.
This shows that it is impossible to make B false and all antecedents (i.e.,
A2, A3, A4, and A5) true at the same time, and thus A2 ??§ A3 ??§ A4 ??§
A5 ??? B is a tautology. That is, the policies represented by A2, A3, and
A4, and the fact represented by A5 dictate that the drug should not be
175
Appendix B
marketed. It is impossible to market the drug without contradicting A5
or violating at least one of the policies represented by A2, A3, and A4.
Note that the constraints A2??“A5 are consistent in that it is possible to
find an assignment to all propositional variables involved so that all the
constraints are true at the same time.
Pages:
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153