Enabling local computation for partially ordered preferences

Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on the use of partially ordered scales and examines how such scales can be cast in the Shafer-Shenoy framework and thus benefit from local computation algorithms. It also provides several examples of such scales, thus showing that each of the algebraic structures explored here is of interest

Bilattice based Logical Reasoning for Automated Visual Surveillance and other Applications

The primary objective of an automated visual surveillance system is to observe and understand human behavior and report unusual or potentially dangerous activities/events in a timely manner. Automatically understanding human behavior from visual input, however, is a challenging task. The research presented in this thesis focuses on designing a reasoning framework that can combine, in a principled manner, high level contextual information with low level image processing primitives to interpret visual information. The primary motivation for this work has been to design a reasoning framework that draws heavily upon human like reasoning and reasons explicitly about visual as well as non-visual information to solve classification problems. Humans are adept at performing inference under uncertainty by combining evidence from multiple, noisy and often contradictory sources. This thesis describes a logical reasoning approach in which logical rules encode high level knowledge about the world and logical facts serve as input to the system from real world observations. The reasoning framework supports encoding of multiple rules for the same proposition, representing multiple lines of reasoning and also supports encoding of rules that infer explicit negation and thereby potentially contradictory information. Uncertainties are associated with both the logical rules that guide reasoning as well as with the input facts. This framework has been applied to visual surveillance problems such as human activity recognition, identity maintenance, and human detection. Finally, we have also applied it to the problem of collaborative filtering to predict movie ratings by explicitly reasoning about users preferences