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
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