Belief Revision with Uncertain Inputs in the Possibilistic Setting

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. Revision can be based on two possible definitions of the conditioning operation, one based on min operator which requires a purely ordinal scale only, and another based on product, for which a richer structure is needed, and which is a particular case of Dempster's rule of conditioning. Besides, revision under uncertain inputs can be understood in two different ways depending on whether the input is viewed, or not, as a constraint to enforce. Moreover, it is shown that M.A. Williams' transmutations, originally defined in the setting of Spohn's functions, can be captured in this framework, as well as Boutilier's natural revision.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Numerical Representations of Acceptance

Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of acceptance, what we call acceptance functions. Due to the monotonicity property of confidence measures, the acceptance of a proposition entails the acceptance of any of its logical consequences. In agreement with the idea that a belief set (in the sense of Gardenfors) must be closed under logical consequence, it is also required that the separate acceptance o two propositions entail the acceptance of their conjunction. Necessity (and possibility) measures agree with this view of acceptance while probability and belief functions generally do not. General properties of acceptance functions are estabilished. The motivation behind this work is the investigation of a setting for belief revision more general than the one proposed by Alchourron, Gardenfors and Makinson, in connection with the notion of conditioning.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

An Ordinal View of Independence with Application to Plausible Reasoning

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, and a complete axiomatization is provided for the strongest one. Moreover we show that weak independence is well-suited to the problems of belief change and plausible reasoning, especially to address the problem of blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

A New Rational Algorithm for View Updating in Relational Databases

The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In order to apply the rationality result of belief dynamics theory to various practical problems, it should be generalized in two respects: first it should allow a certain part of belief to be declared as immutable; and second, the belief state need not be deductively closed. Such a generalization of belief dynamics, referred to as base dynamics, is presented in this paper, along with the concept of a generalized revision algorithm for knowledge bases (Horn or Horn logic with stratified negation). We show that knowledge base dynamics has an interesting connection with kernel change via hitting set and abduction. In this paper, we show how techniques from disjunctive logic programming can be used for efficient (deductive) database updates. The key idea is to transform the given database together with the update request into a disjunctive (datalog) logic program and apply disjunctive techniques (such as minimal model reasoning) to solve the original update problem. The approach extends and integrates standard techniques for efficient query answering and integrity checking. The generation of a hitting set is carried out through a hyper tableaux calculus and magic set that is focused on the goal of minimality.Comment: arXiv admin note: substantial text overlap with arXiv:1301.515

Paradox Elimination in Dempster–Shafer Combination Rule with Novel Entropy Function: Application in Decision-Level Multi-Sensor Fusion

Multi-sensor data fusion technology in an important tool in building decision-making applications. Modified Dempster–Shafer (DS) evidence theory can handle conflicting sensor inputs and can be applied without any prior information. As a result, DS-based information fusion is very popular in decision-making applications, but original DS theory produces counterintuitive results when combining highly conflicting evidences from multiple sensors. An effective algorithm offering fusion of highly conflicting information in spatial domain is not widely reported in the literature. In this paper, a successful fusion algorithm is proposed which addresses these limitations of the original Dempster–Shafer (DS) framework. A novel entropy function is proposed based on Shannon entropy, which is better at capturing uncertainties compared to Shannon and Deng entropy. An 8-step algorithm has been developed which can eliminate the inherent paradoxes of classical DS theory. Multiple examples are presented to show that the proposed method is effective in handling conflicting information in spatial domain. Simulation results showed that the proposed algorithm has competitive convergence rate and accuracy compared to other methods presented in the literature