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Modal Logic is a branch of logic with applications in many related
disciplines such as computer science, philosophy, linguistics and
artificial intelligence. Over the last twenty years, in all of
these neighbouring fields, modal systems have been developed that
we call multi-dimensional. (Our definition of multi-dimensionality
in modal logic is a technical one: we call a modal formalism
multi-dimensional if, in its intended semantics, the universe of a
model consists of states that are tuples over some more basic set.)
This book treats such multi-dimensional modal logics in a uniform
way, linking their mathematical theory to the research tradition in
algebraic logic. We will define and discuss a number of systems in
detail, focusing on such aspects as expressiveness, definability,
axiomatics, decidability and interpolation. Although the book will
be mathematical in spirit, we take care to give motivations from
the disciplines mentioned earlier on.
Finite model theory,as understoodhere, is an areaof
mathematicallogic that has developed in close connection with
applications to computer science, in particular the theory of
computational complexity and database theory. One of the
fundamental insights of mathematical logic is that our
understanding of mathematical phenomena is enriched by elevating
the languages we use to describe mathematical structures to objects
of explicit study. If mathematics is the science of patterns, then
the media through which we discern patterns, as well as the
structures in which we discern them, command our attention. It
isthis aspect oflogicwhichis mostprominentin model
theory,"thebranchof mathematical logic which deals with the
relation between a formal language and its interpretations". No
wonder, then, that mathematical logic, and ?nite model theory in
particular, should ?nd manifold applications in computer science:
from specifying programs to querying databases, computer science is
rife with phenomena whose understanding requires close attention to
the interaction between language and structure. This volume gives a
broadoverviewof some central themes of ?nite model theory:
expressive power, descriptive complexity, and zero-one laws,
together with selected applications to database theory and
arti?cial intelligence, es- cially constraint databases and
constraint satisfaction problems. The ?nal chapter provides a
concise modern introduction to modal logic,which emp- sizes the
continuity in spirit and technique with ?nite model theory.
Modal Logic is a branch of logic with applications in many related
disciplines such as computer science, philosophy, linguistics and
artificial intelligence. Over the last twenty years, in all of
these neighbouring fields, modal systems have been developed that
we call multi-dimensional. (Our definition of multi-dimensionality
in modal logic is a technical one: we call a modal formalism
multi-dimensional if, in its intended semantics, the universe of a
model consists of states that are tuples over some more basic set.)
This book treats such multi-dimensional modal logics in a uniform
way, linking their mathematical theory to the research tradition in
algebraic logic. We will define and discuss a number of systems in
detail, focusing on such aspects as expressiveness, definability,
axiomatics, decidability and interpolation. Although the book will
be mathematical in spirit, we take care to give motivations from
the disciplines mentioned earlier on.
Advances in Modal Logic is a unique international forum for
presenting the latest results and new directions of research in
modal logic broadly conceived. The topics dealt with are of
interdisciplinary interest and range from mathematical,
computational, and philosophical problems to applications in
knowledge representation and formal linguistics. This volume
contains invited and contributed papers from the sixth conference
in the series, held for the first time outside Europe, in Noosa,
Queensland, Australia, in September 2006. It reports on
considerable progress, both in the foundations of modal logic and
in a number of application areas. It includes papers on the theory
of modal logic itself, on process theory, multi-agent systems and
spatial reasoning, and work on quantified modal logic, modal
reasoning methods, and philosophical issues.
This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects. Applications to issues in logic and computer science such as completeness, computability and complexity are considered.
Finite model theory,as understoodhere, is an areaof
mathematicallogic that has developed in close connection with
applications to computer science, in particular the theory of
computational complexity and database theory. One of the
fundamental insights of mathematical logic is that our
understanding of mathematical phenomena is enriched by elevating
the languages we use to describe mathematical structures to objects
of explicit study. If mathematics is the science of patterns, then
the media through which we discern patterns, as well as the
structures in which we discern them, command our attention. It
isthis aspect oflogicwhichis mostprominentin model
theory,"thebranchof mathematical logic which deals with the
relation between a formal language and its interpretations". No
wonder, then, that mathematical logic, and ?nite model theory in
particular, should ?nd manifold applications in computer science:
from specifying programs to querying databases, computer science is
rife with phenomena whose understanding requires close attention to
the interaction between language and structure. This volume gives a
broadoverviewof some central themes of ?nite model theory:
expressive power, descriptive complexity, and zero-one laws,
together with selected applications to database theory and
arti?cial intelligence, es- cially constraint databases and
constraint satisfaction problems. The ?nal chapter provides a
concise modern introduction to modal logic,which emp- sizes the
continuity in spirit and technique with ?nite model theory.
Labelled transition systems are mathematical models for dynamic
behaviour, or processes, and thus form a research field of common
interest to logicians and theoretical computer scientists. In
computer science, this notion is a fundamental one in the formal
analysis of programming languages, in particular in process theory.
In modal logic, transition systems are the central object of study
under the name of Kripke models. This volume collects a number of
research papers on modal logic and process theory. Its unifying
theme is the notion of a bisimulation. Bisimulations are relations
over transition systems, and provide a key tool in identifying the
processes represented by these structures. The volume offers an
up-to-date overview of perspectives on labelled transition systems
and bisimulations.
Labelled transition systems are mathematical models for dynamic
behaviour, or processes, and thus form a research field of common
interest to logicians and theoretical computer scientists. In
computer science, this notion is a fundamental one in the formal
analysis of programming languages, in particular in process theory.
In modal logic, transition systems are the central object of study
under the name of Kripke models. This volume collects a number of
research papers on modal logic and process theory. Its unifying
theme is the notion of a bisimulation. Bisimulations are relations
over transition systems, and provide a key tool in identifying the
processes represented by these structures. The volume offers an
up-to-date overview of perspectives on labelled transition systems
and bisimulations.
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