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Finite Model Theory and Its Applications (Paperback, 2007 ed.)
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Finite Model Theory and Its Applications (Paperback, 2007 ed.)
Series: Texts in Theoretical Computer Science. An EATCS Series
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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.
General
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