Generic Inference A Unifying Theory for Automated Reasoning

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 ▲]

Generalized Information Theory based on the Theory of Hints

in Liu, Weiru (Ed.) Symbolic and Quantitative Approaches to Reasoning with Uncertainty (2011)

The aggregate uncertainty is the only known functional for Dempster-Shafer theory that generalizes the Shannon and Hartley mea- sures and satis?es all classical requirements for uncertainty measures ... [more ▼]

The aggregate uncertainty is the only known functional for Dempster-Shafer theory that generalizes the Shannon and Hartley mea- sures and satis?es all classical requirements for uncertainty measures, including subadditivity. Although being posed several times in the liter- ature, it is still an open problem whether the aggregate uncertainty is unique under these properties. This paper derives an uncertainty measure based on the theory of hints and shows its equivalence to the pignistic entropy. It does not satisfy subadditivity, but the viewpoint of hints un- covers a weaker version of subadditivity. On the other hand, the pignistic entropy has some crucial advantages over the aggregate uncertainty. i.e. explicitness of the formula and sensitivity to changes in evidence. We observe that neither of the two measures captures the full uncertainty of hints and propose an extension of the pignistic entropy called hints en- tropy that satis?es all axiomatic requirements, including subadditivity, while preserving the above advantages over the aggregate uncertainty. [less ▲]

Computational Aspects of Attack-Defense Trees

in Security and Intelligent Information Systems - International Joint Conferences, SIIS 2011, Warsaw, Poland, June 13-14, 2011, Revised Selected Papers (2011)

Attack-defense trees extend attack trees with defense nodes. This richer formalism allows for a more precise modeling of a system’s vulnerabilities, by representing interactions between possible attacks ... [more ▼]

Attack-defense trees extend attack trees with defense nodes. This richer formalism allows for a more precise modeling of a system’s vulnerabilities, by representing interactions between possible attacks and corresponding defensive measures. In this paper we compare the computational complexity of both formalisms. We identify semantics for which extending attack trees with defense nodes does not increase the computational complexity. This implies that, for these semantics, every query that can be solved efficiently on attack trees can also be solved efficiently on attack-defense trees. Furthermore, every algorithm for attack trees can directly be used to process attack-defense trees. [less ▲]