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Logics of Knowledge and Belief

Keywords: possible worlds

Categories: Inference and Reasoning , Knowledge Representation


Author(s): Colin Phillips

In order to construct a plan it is often necessary for an agent to take into account the possibility that certain pieces of knowledge may be required to execute the plan: knowledge which may be obtainable by performing certain actions. An agent may also need to take into account the knowledge and beliefs of other agents. So in designing an intelligent agent we need to employ some method for reasoning about knowledge and belief. A logic of knowledge or belief can be obtained by adding to some system of logic some means of expressing such facts as `A knows that p ' or `A believes that p ' where `A ' designates an agent and `p ' a proposition. So we could introduce names of agents and variables ranging over agents together with operators such as K and B , so that `K(A,p) ' means that A knows that p and `B(A,p) ' means that A believes thatp

. In AI there are basically two approaches to the construction of a logic of knowledge or belief. There is a sentential approach where we associate with each agent a set of sentences which constitutes the agent's base beliefs. We say that an agent believes a proposition exactly if the agent can prove the proposition from these base beliefs. An agent knows a proposition if he or she believes the proposition and it is true. There is also an approach which construes the K operator as analogous to the L operator in Modal Logic. Here we associate with each agent sets of possible worlds. We say that an agent believes a proposition in a given world just in case that proposition holds in every world accessible for an agent in a given world.


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