The LOP shows that the view that modal epistemic logic describes actual knowledge of idealized agents is not tenable. A certain degree of idealization is meaningful and even necessary in philosophical and scientific research. However, the idealizations made by modal epistemic logic are so strong that the agents they describe have hardly anything in common with real agents. Those ``agents'' are merely theoretical constructs without any empirical basis. Hence, the modal approach is not suited to capturing the notion of actual knowledge (or belief) adequately.
But if modal epistemic logics do not describe what agents actually know, what do they describe then? Well, they can be interpreted as logics of a related, but different concept. It is remarked by several authors that the laws of modal systems are acceptable if the formula is read ``agent knows implicitly'' ([Lev84], [FH88],) `` follows from 's knowledge'' ([FHMV95]), ``agent carries the information '' ([Bar89]), or `` is agent 's possible knowledge'' ([HK91]), instead of ``the agent knows ''. Although the technical definitions may differ, ``implicit knowledge'' and similar terms are all used in the same spirit: they refer to what is implicitly represented in an agent's information state, i.e., what logically follows from his actual knowledge. They describe dispositional states which could only be established by reasoning and reflection upon one's mental states. The concept of implicit knowledge is used without any notion of agents computing knowledge or having to answer questions based on their knowledge. What an agent actually knows is called his explicit knowledge.
If ``knowledge'' is understood as ``implicit knowledge'', then the forms of logical omniscience discussed previously are no longer a problem: although the discussed axioms and inference rules are not reasonable for the explicit view, they are acceptable for the implicit view of knowledge. Thus, modal epistemic logics seem to be acceptable for the purpose of formalizing the concept of implicit knowledge. They should be interpreted as logics of implicit, or potential knowledge, and not as logics of explicit, or actual knowledge.
From the viewpoint of agent theories, actual (explicit) knowledge is clearly more important than implicit knowledge: it is the former kind of knowledge that agents can act upon, but not the latter. The mere implicit knowledge that some path connecting all towns in a region is the shortest one is useless for a traveling salesman who seeks to maximize his profit -- he must make this implicit knowledge explicit in order to choose what path to travel. The implicit, but not explicit knowledge of a winning strategy is useless for a chess player who must make the next move within a short time. An information agent whose knowledge is represented as a knowledge base must normally make complex and time-consuming inferences before he can answer a query.
Since agents need to act on the basis what they actually know, and not what they merely potentially know, agent theories must be based on logics that can capture what agents actually know. Because of the importance of explicit knowledge for agents' action, the search for logics of explicit knowledge has been continuing, and a number of systems have been proposed for that purpose. In the next chapter I shall review the most important attempts to model explicit knowledge and show why they are not suitable as a basis for agent theories.