Abstract mathematical structures usually have a large number of models. Algorithms
based on operations and laws of such structures therefore have an identical form:
they are generic. This means that for each particular instance of the structure, only
the basic operations have to be adapted, whereas the overall algorithm remains the
same. The simplest and typical problem is the one of sorting. It applies to totally
ordered structures with an order relation <. Any sorting algorithm can be formulated
in terms of the order relation < and it can be adapted to any particular model of an
order relation by specifying this relation; for example for integers, real numbers or for
a lexicographical order relation of alphanumeric strings. In addition, many programming
languages allow for generic programming, i.e. in their syntax they provide the
means to formulate generic algorithms and to specialize them to particular instances.
In this book, an abstract algebraic structure called valuation algebra is proposed.
It provides the foundation to formulate an abstract inference problem, to construct
a graphical data structure and a generic inference algorithm to solve the inference
This book provides a rigorous algebraic study of the most popular inference formalisms with a special focus on their wide application area, showing that all these tasks can be performed by a single generic inference algorithm. Written by the leading international authority on the topic, it includes an algebraic perspective (study of the valuation algebra framework), an algorithmic perspective (study of the generic inference schemes) and a "practical" perspective (formalisms and applications). Researchers in a number of fields including artificial intelligence, operational research, databases and other areas of computer science; graduate students; and professional programmers of inference methods will benefit from this work.
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