Contents

• Acknowledgments
• Contents
• Introduction
  • Motivation
  • Structure of the thesis
  • Main results
  • Notations and preliminaries
• Modal epistemic logic
  • The ``received view'': modal epistemic logic
    • The language of epistemic logic
    • Axioms for modal epistemic logic
    • Possible-worlds semantics for epistemic logic
  • Adding common knowledge
  • Epistemic logic and agent theories
  • The problem of logical omniscience
    • Implicit knowledge
• Other models of knowledge
  • Logics for non-omniscient agents
    • Weak deduction mechanisms
    • Impossible possible worlds
    • Awareness
  • Logical omniscience vs. logical ignorance
• Explicit knowledge
  • The dynamics of knowledge
    • Explicit knowledge and reasoning actions
    • The abstract action of reasoning
  • Dynamic epistemic logic
    • The language of dynamic-epistemic logic
    • Axioms for dynamic-epistemic logic
    • Systems of dynamic-epistemic logic
    • Some features of dynamic-epistemic logic
    • Systems with the directedness axiom
• Algorithmic knowledge
  • Motivation
    • Why explicit knowledge is not enough
    • The language of algorithmic knowledge
  • Reasoning about algorithmic knowledge
    • Axioms for algorithmic knowledge
    • Logics of algorithmic knowledge
    • Knowledge and complexity
    • Complexity and the lack of knowledge
  • Modeling resources other than time
• Conclusion
  • Summary
  • Related works
  • Future directions
• Propositional modal, temporal, and dynamic logic
  • Modal logic
    • Sytax of modal logic
    • Semantics for normal modal logic: Kripke models
    • Montague-Scott semantics
    • Basic temporal logic
  • Propositional Dynamic Logic
• Formal Proofs
  • Theorem 21
  • Theorem 22
  • Theorem 28
• Bibliography
• About this document ...