In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Robust belief revision methods are crucial in streaming data situations for updating existing knowledge (or beliefs) with new incoming evidence. Bayes conditioning is the primary mechanism in use for belief revision in data fusion systems that use probabilistic inference. However, traditional conditioning methods face several challenges due to inherent data/source imperfections in big-data environments that harness soft (i.e., human or human-based) sources in addition to hard (i.e., physicsbased) sensors. The objective of this paper is to investigate the most natural extension of Bayes conditioning that is suitable for evidence updating in the presence of such uncertainties. By viewing the evidence updating process as a thought experiment, an elegant strategy is derived for robust evidence updating in the presence of extreme uncertainties that are characteristic of big-data environments. In particular, utilizing the Fagin-Halpern conditional notions, a natural extension to Bayes conditioning is derived for evidence that takes the form of a general belief function. The presented work differs fundamentally from the Conditional Update Equation (CUE) and authors own extensions of it. An overview of this development is provided via illustrative examples. Furthermore, insights into parameter selection under various fusion contexts are also provided.
Evidence Updating for Stream-Processing in Big-Data: Robust Conditioning in Soft and Hard Data Fusion Environments

Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined complexity can be arbitrarily high. Furthermore, we prove that all the rule languages with finite chase that extend the weakly acyclic language are of the same expressiveness as the weakly acyclic one, while rule languages with higher combined complexity are in general more succinct than those with lower combined complexity.
Existential Rule Languages with Finite Chase: Complexity and Expressiveness

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize Chisholm's system by grounding his undefined and primitive (i.e. foundational) concept of reasonableness in probability and proof theory. S can be useful in systems that have to interact with humans and provide justifications for their uncertainty. As a demonstration of the system, we apply the system to provide a solution to the lottery paradox. Another advantage of the system is that it can be used to provide uncertainty values for counterfactual statements. Counterfactuals are statements that an agent knows for sure are false. Among other cases, counterfactuals are useful when systems have to explain their actions to users (If I had not done , then would have happened). Uncertainties for counterfactuals fall out naturally from our system. Efficient reasoning in just simple first-order logic is a hard problem. Resolution-based first-order reasoning systems have made significant progress over the last several decades in building systems that have solved non-trivial tasks (even unsolved conjectures in mathematics). We present a sketch of a novel algorithm for reasoning that extends firstorder resolution. Finally, while there have been many systems of uncertainty for propositional logics, first-order logics and propositional modal logics, there has been very little work in building systems of uncertainty for first-order modal logics. The work described below is in progress; and once finished will address this lack.
Strength Factors: An Uncertainty System for a Quantified Modal Logic