Question

AI: For each of the following assertions, say whether it is true or false and support your answer with examples or counterexamples where appropriate.
a. An agent that senses only partial information about the state cannot be perfectly rational.
b. There exist task environments in which no pure reflex agent can behave rationally.
c. There exists a task environment in which every agent is rational.
d. The input to an agent program is the same as the input to the agent function.
e. Every agent function is implementable by some program/machine combination.
f. Suppose an agent selects its action uniformly at random from the set of possible actions. There exists a deterministic task environment in which this agent is rational.
g. It is possible for a given agent to be perfectly rational in two distinct task environments.
h. Every agent is rational in an unobservable environment.
i. A perfectly rational poker-playing agent never loses.

Answer 1

(a) This is FALSE. If the agent is working only on the partial state of the environment, it need not know about the entire environment.

(b) This is TRUE. If there is need of memory, then the reflex agent will face trouble in such cases and won't be rational.

(c) TRUE. If in an environment, all the actions result in rewards which is same and equal for all. Then it is such a case where every agent is rational. Notice that all actions also includes the "no action" case.

(d) FALSE. Agent program's input is the current percept while the agent function's input is the percept history. So, the agent program decides whether to record any relevant history or not in order to take actions.

(e) FALSE. If an agent exists which returns an integer and perceives a bit each time it returns an integer. Then if the integer returned matches the perceived bits, then it increases a performance point. This will eventually cause short of memory and agent will fail.

(f) TRUE because if we consider a case where we have a number of actions and all of them are giving the same result, then we can see clearly that this statement is true.

(g) TRUE. One example to show that it is possible could be two instances of a tossing the coin game. In one instance, a fair coin is used and in the other instance, an unfair coin is used. If the agent chooses the baised side of the unfair coin in both the games, then it is optimal for both cases. So, such a statement is true.

(h) FALSE. This is because if there is built in data about the environment, then the agent can work properly but in an unobserved environment, there is no such data.

(i) FALSE. Assume there are two perfectly playing agents. If they are put against each other, one of them will win and other one would lose. Thus, it is false to say that a perfectly playing agent can't lose.