The relation between logic(s) and Artificial Intelligence became very strong and important in the past two decades, and considering the two areas independent of each other, there is an increasing mutual benefit. “Very theoretic, purely logic” theories with a strong philosophical background were applied to real-world problems, but also the modelling of real problems and areas led to new developments in many “logic fields”. And the main problem, naturally, for these interdisciplinary relations is the question how an applied scientist can improve his knowledge in logic, or how logic can be taught in such a way that it is available for solving applied problems. And especially here the presented text makes a very serious contribution.
Even if there can be some doubts whether the target group of the text really can be undergraduate students, the representation shows the high pedagogic and scientific skills of the authors.
The different chapters deal very carefully with the following topics:
\(\blacksquare\)an introduction to epistemic logic,
\(\blacksquare\)the modal basics of multi-agent epistemic logic, including Kripke
\(\phantom{\blacksquare}\)semantics,
\(\blacksquare\)the application to distributed systems and to protocol verification,
\(\blacksquare\)various concepts of knowledge and belief (common knowledge in
\(\phantom{\blacksquare}\)distributed systems, implicit knowledge in a group, logical omniscience,
\(\phantom{\blacksquare}\)implicit and explicit belief, local reasoning and opaque knowledge etc.).
The whole third chapter changes the point of view and asks what can be said about the ignorance of an agent. Again the presented material is very rich and bridges the gap to the recent research areas (the theory of honesty of Halpern & Moses, nonmonotonic reasoning and preferential entailment, autoepistemic logic of Moore).
The final fourth chapter shows default and counterfactual reasoning on the base of epistemic logic.
The appendices deepen the consideration of special problems:
\(\blacksquare\)Konolige’s deduction model of belief,
\(\blacksquare\)knowledge structures,
\(\blacksquare\)first-order epistemic logic.
The book is very rich in exercises, and all the exercises are answered on 100 additional pages giving pretty good chances to understand and to apply the theories.
As an important prerequisite, the book needs a very good understanding of classical propositional and predicate calculi and a high-level formal training. Who goes through the book in a hard-working way will find an interesting text and get a lot of benefit.