The thesis is organized as follows. First, I shall review briefly the possible-worlds approach to epistemic logic and its relationship to recent agent theories in chapter 2. I shall show that the modal approach can at most account for the concept of implicit knowledge, but that concept is not helpful in describing agents, simply because agents need to act upon what they explicitly know, and not what they merely implicitly know.
In chapter 3 I examine some influential alternative approaches to epistemic logic and evaluate how they may be suited to describing realistic agents. I shall show that almost all attempts proposed in the literature to overcome the difficulties of the modal approach consist in weakening the standard epistemic systems. That is, weaker systems are considered where the agents do not possess the full reasoning capacities of ideal reasoners. I shall argue that those alternatives are not satisfactory because they restrict the agents' intelligence arbitrarily, so the intuition that agents are rational gets lost. Consequently, they are not suitable for formalizing the informational aspect of intelligent agents.
In chapter 4 a framework for reasoning about explicit knowledge will be developed. I shall show that axioms for explicit knowledge must have the following form: if the agent knows all premises of a valid inference rule, and if he thinks hard enough, then he will know the conclusion. To formalize such an idea, I propose to introduce a dynamic component into the epistemic language. I shall show that my approach offers an intuitive solution to the logical omniscience problem while preserving the intuition that agents are rational. My approach is therefore is suitable for formalizing the notion of actual, or explicit knowledge.
In chapter 5 I shall develop logics of algorithmic knowledge -- a new concept of knowledge which generalizes both implicit and explicit knowledge. The main idea is to combine epistemic logic with a complexity analysis: we consider how long an agent will need to compute the solution to a certain problem. After explaining the underlying intuitions I shall introduce the concept of algorithmic knowledge and develop formal theories of this new concept.
A short overview of modal, temporal, and dynamic logic is given in appendix A. Formal proofs of some theorems are found in appendix B.