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Second-order Quantifier Elimination - Foundations, Computational Aspects and Applications (Paperback, New)
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Second-order Quantifier Elimination - Foundations, Computational Aspects and Applications (Paperback, New)
Series: Studies in Logic: Mathematical Logic and Foundations, v. 12
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In recent years there has been an increasing use of logical methods
and significant new developments have been spawned in several areas
of computer science, ranging from artificial intelligence and
software engineering to agent-based systems and the semantic web.
In the investigation and application of logical methods there is a
tension between: * the need for a representational language strong
enough to express domain knowledge of a particular application, and
the need for a logical formalism general enough to unify several
reasoning facilities relevant to the application, on the one hand,
and * the need to enable computationally feasible reasoning
facilities, on the other hand. Second-order logics are very
expressive and allow us to represent domain knowledge with ease,
but there is a high price to pay for the expressiveness. Most
second-order logics are incomplete and highly undecidable. It is
the quantifiers which bind relation symbols that make second-order
logics computationally unfriendly. It is therefore desirable to
eliminate these second-order quantifiers, when this is
mathematically possible; and often it is. If second-order
quantifiers are eliminable we want to know under which conditions,
we want to understand the principles and we want to develop methods
for second-order quantifier elimination. This book provides the
first comprehensive, systematic and uniform account of the
state-of-the-art of second-order quantifier elimination in
classical and non-classical logics. It covers the foundations, it
discusses in detail existing second-order quantifier elimination
methods, and it presents numerous examples of applications and
non-standard uses in different areas. These include: * classical
and non-classical logics, * correspondence and duality theory, *
knowledge representation and description logics, * commonsense
reasoning and approximate reasoning, * relational and deductive
databases, and * complexity theory. The book is intended for anyone
interested in the theory and application of logics in computer
science and artificial intelligence.
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