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See detailGeneric Inference A Unifying Theory for Automated Reasoning
Pouly, Marc UL; Kohlas, Jürg

Book published by John Wiley & Sons (2011)

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 ... [more ▼]

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. [less ▲]

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See detailGeneric Local Computation
Pouly, Marc UL; Schneuwly, Cesar; Kohlas, Jürg

Report (2011)

Many problems of artificial intelligence, or more generally, many problems of information processing, have a generic solution based on local computation on join trees or acyclic hypertrees. There are ... [more ▼]

Many problems of artificial intelligence, or more generally, many problems of information processing, have a generic solution based on local computation on join trees or acyclic hypertrees. There are several variants of this method all based on the algebraic structure of a valuation algebra. A strong requirement underlying this approach is that the elements of a problem decomposition form a join tree. Although it is always possible to construct covering join trees, if the requirement is originally not satisfied, it is not always possible or not efficient to extend the elements of the decomposition to the covering join tree. Therefore in this paper different variants of an axiomatic framework of valuation algebras are introduced which prove sufficient for local computation without the need of an extension of the factors of a decomposition. This framework covers the axiomatic system proposed by (Shenoy & Shafer, 1990). A particular emphasis is laid on the important special cases of idempotent algebras and algebras with some notion of division. It is shown that all well-known architectures for local computation like the Shenoy-Shafer architecture, Lauritzen-Spiegelhalter and HUGIN architectures may be adapted to this new framework. Further a new architecture for idempotent algebras is presented. As examples, in addition to the classical instances of valuation algebras, semiring induced valuation algebras, Gaussian potentials and the relational algebra are presented. [less ▲]

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