TODO: see Probability
trying to use classical logic to cope with a domain like medical diagnosis thus fails for three main reasons:
- laziness: it is too much work to list the complete set of antecedents or consequents needed to ensure an exceptionless rule and too hard to use such rules
- ignorance - lack of knowledge or information
- theoretical ignorance: medical science has no complete theory for the domain
- practical ignorance: even if we know all the rules, we might be uncertain about a particular patient because not all the necessary tests have been or can be run
classical logic has a qualification problem - the impossibility of listing all the preconditions required for a real-world action to have its intended effect
probability provides a way of summarizing the uncertainty that comes from our laziness and ignorance
classical logic statements are made with respect to the real world
probability statements are made with respect to a knowledge state, not to the real world
Uncertainty and Rational Decisions
Consider the A90plan for getting to the airport (leaving home 90 minutes before the flight departs and driving at a reasonable speed). Suppose it gives us a 97% chance of catching our flight. Does this mean it is a rational choice? Not necessarily: there might be other plans, such as A180, with higher probabilities. If it is vital not to miss the flight, then it is worth risking the longer wait at the airport. What about A1440, a plan that involves leaving home 24 hours in advance? In most circumstances, this is not a good choice, because although it almost guarantees getting there on time, it involves an intolerable wait—not to mention a possibly unpleasant diet of airport food.
To make such choices, an agent must have preferences between different outcomes (a completely specified state) of various plans.
Representing and Reasoning Preferences
utility theory
- used to represent preferences and reasoning with it
- utility means “the quality of being useful”
- the utility of a outcome/state is relative to an agent
- a utility function accounts for any set of preferences
Theory of Rational Decisions
decision theory
- decision-theory = probability-theory + utility-theory
- fundamental idea of decision theory is that an agent is rational if and only if it chooses an action of maximum expected utility (MEU)
- maximum expected utility (MEU) - choosing an action out of a set of all possible actions in current state that yields the highest expected utility (an average over all the possible outcomes of the action)
- a decision-theoretic agent’s belief state represents not just the possibilities for world states but also their probabilities