PossibleWorlds

• Originally proposed by Hintikka in 1962.
• Now is commonly modeled using modal logic developed by Kripke in 1963.

An agent is playing poker. Complete knowledge of the opponents hand is impossible to determine. The ability to play is determined partially by the agent's belief in the opponents hand. Suppose agent has Ace of Spades. First compute all the possible ways the cards could be dealt to the opponent. These are possible worlds. Then eliminate those worlds that are not possible given what the agent knows. What is left over are the epistemic alternatives (worlds possbile given ones beliefs). Something TRUE in all worlds is said to be believed by the agent (It is TRUE that the agent has the Ace of Spades).

Normal Modal Logic for Possible Worlds

• Classical propositional logic extended by 2 operators. "" (necessarily) and "" (possibly).
• The semantics of modal connectives define what worlds are considered accessible from other worlds.
• The formulae is then TRUE if is TRUE for all worlds accessible from the current world.
• The formulae is TRUE if is TRUE for in at least one world accessible from the current world.
• The two modal operators are duals of each other:

		[IntentionalNotions | BeliefDesireIntention | NormalModalLogic]