I consider the book Deductive Systems and the Decidability Problem for Hybrid Logic as (…) a very reliable survey on the issue of computational complexity of hybrid logics, which, additionaly, makes a significant contribution to this area of research."„Worth stressing is the fact that the author shows great expertise in the topic referring to extensive literature."„(The book) presents the syntax, ... Read morethe semantics, the expressive power and the computational complexity of the satisfiability problem for hybrid logics. The author proves the results on the axiomatizability and the computational complexity of selected non-standard hybrid logics. Apart from the indicated important metalogical problems, the book contains a whole range of theorems on the existence of the finite model property for selected hybrid logics."„The results of the second part of the book concern deductive systems (tableau and sequent) for standard and non-standard hybrid logics. The results reported in this part comprise devising two tableau calculi – internalized (…) and prefixed (…) – and investigating their soundness and completeness for a wide class of both standard and non-standard hybrid logics."„The book is devoted to several very interesting issues. The author provides a general introduction to hybrid logics. Since he is interested in the problem of decidability for these logics, he selects some of them, presents all necessary tools used in the proofs and, finally, he establishes the complexity class for a given logic. On this occasion, considering various tableau and sequent calculi for these logics, he investigates many proof-theoretical issues, in particular several blocking mechanisms and restrictions that can be put on the application of rules.
Marek Nasieniewski, Nicolaus Copernicus University Show Less