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Acknowledgments
Contents
Resource-Bounded Reasoning about Knowledge
Dipl.Inf.
Ho Ngoc Duc
April 2001
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 ...
2001-04-05
