Generic Inference: A Unifying Theory for Automated Reasoning

This unique text provides a complete algebraic and algorithmic study of generic inference methods that are derived from the general valuation algebra framework, with special focus on the many practical applications in computer science. Written by the leading international authorities on the topic, Generic Inference is divided into three parts:

• Part I defines the valuation algebra framework and gives a first catalog of practically important examples; explains the generic inference problem and surveys fundamental applications that require the solution of such problems with knowledge bases from different valuation algebras; develops generic algorithms for the solution of single- and multiple-query inference problems with arbitrary valuation algebras; and discusses issues related to complexity and optimization

• Part II identifies several important families of valuation algebras derived from other mathematical structures—including soft constraints, path problems, linear systems, and logical structures—and uncovers the close relationship between valuation algebras and semiring theory

• Part III discusses various applications of generic inference, with chapters dedicated to dynamic optimization, sparse matrix techniques, and linear systems with stochastic disturbances

The text is accompanied by a large number of examples; at the end of every chapter are selected exercises and open research problems. A comprehensive bibliography on valuation algebras and local computation is provided, and all algorithms are developed mathematically and given in pseudo-code. Generic Inference is designed for researchers in a number of fields, including artificial intelligence, operational research, databases, and other areas of computer science; graduate students and other researchers interested in general reasoning frameworks; and professional programmers of inference methods.

This unique text provides a complete algebraic and algorithmic study of generic inference methods that are derived from the general valuation algebra framework, with special focus on the many practical applications in computer science. Written by the leading international authorities on the topic, Generic Inference is divided into three parts:

• Part I defines the valuation algebra framework and gives a first catalog of practically important examples; explains the generic inference problem and surveys fundamental applications that require the solution of such problems with knowledge bases from different valuation algebras; develops generic algorithms for the solution of single- and multiple-query inference problems with arbitrary valuation algebras; and discusses issues related to complexity and optimization

• Part II identifies several important families of valuation algebras derived from other mathematical structures―including soft constraints, path problems, linear systems, and logical structures―and uncovers the close relationship between valuation algebras and semiring theory

• Part III discusses various applications of generic inference, with chapters dedicated to dynamic optimization, sparse matrix techniques, and linear systems with stochastic disturbances

The text is accompanied by a large number of examples; at the end of every chapter are selected exercises and open research problems. A comprehensive bibliography on valuation algebras and local computation is provided, and all algorithms are developed mathematically and given in pseudo-code. Generic Inference is designed for researchers in a number of fields, including artificial intelligence, operational research, databases, and other areas of computer science; graduate students and other researchers interested in general reasoning frameworks; and professional programmers of inference methods.