By
A. Kurucz, King's College, London, UK
F. Wolter, University of Liverpool, UK
M. Zakharyaschev, King's College, London, UK
Dov M. Gabbay, King's College London, UK
Description
Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence,
the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are
used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the
nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason
about knowledge bases developing in time or moving objects.
To study the computational behaviour of many-dimensional modal logics
is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while
on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics
with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so
their computational behaviour can be analyzed using the developed machinery.
We start with concrete examples of applied one- and
many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then
we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics,
fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational
complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings,
reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results
to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent
systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.
The genre of the book can be defined as
a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and
directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order
logic are formulated without proofs and supplied with references to accessible sources.
The intended audience of this book is logicians
as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g.,
knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And
we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems,
will benefit from this book as well.
Key Features:
• Integrated approach to modern modal and temporal logics and their applications
in artificial intelligence and computer science
• Written by internationally leading researchers in the field of pure and applied
logic
• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science
•
Numerous open problems for further research
• Well illustrated with pictures and tables
Included in series
Studies in Logic and the Foundations of Mathematics
Audience:
Logicians. Logicians in Computer Science (reseachers and students). Researchers and students in knowledge representation and reasoning.
