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Generalized Belief Function: A new concept for uncertainty modelling and processing

arXiv.org Artificial Intelligence

In this paper, we generalize the belief function on complex plane from another point of view. We first propose a new concept of complex mass function based on the complex number, called complex basic belief assignment, which is a generalization of the traditional mass function in Dempster-Shafer evidence theory. On the basis of the de nition of complex mass function, the belief function and plausibility function are generalized. In particular, when the complex mass function is degenerated from complex numbers to real numbers, the generalized belief and plausibility functions degenerate into the traditional belief and plausibility functions in DSE theory, respectively.


Multiagent Knowledge and Belief Change in the Situation Calculus

AAAI Conferences

Belief change is an important research topic in AI. It becomes more perplexing in multi-agent settings, since the action of an agent may be partially observable to other agents. In this paper, we present a general approach to reasoning about actions and belief change in multi-agent settings. Our approach is based on a multi-agent extension to the situation calculus, augmented by a plausibility relation over situations and another one over actions, which is used to represent agents' different perspectives on actions. When an action is performed, we update the agents' plausibility order on situations by giving priority to the plausibility order on actions, in line with the AGM approach of giving priority to new information. We show that our notion of belief satisfies KD45 properties. As to the special case of belief change of a single agent, we show that our framework satisfies most of the classical AGM, KM, and DP postulates. We also present properties concerning the change of common knowledge and belief of a group of agents.


Semantic Characterizations of General Belief Base Revision

arXiv.org Artificial Intelligence

The AGM postulates by Alchourr\'on, G\"ardenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. We generalize K&M's approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of "base" (such as belief sets, arbitrary or finite sets of sentences, or single sentences). The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain "assignments": functions mapping belief bases to total - yet not transitive - "preference" relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M's original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence.


Quiet: Faster Belief Propagation for Images and Related Applications

AAAI Conferences

It can be used in image morphing to Belief propagation over Markov random fields has change an image into another through a seamless transition been successfully used in many AI applications in the field of computer art [Lipski et al., 2010]. Other than since it yields accurate inference results by iteratively above, belief propagation is used in a variety of applications updating messages between nodes. However, such as image restoration [Felzenszwalb and Huttenlocher, its high computation costs are a barrier to practical 2006], computer-assisted colorization [Noma et al., 2009], use. This paper presents an efficient approach to and image segmentation [Zhao et al., 2014]. We omit detail belief propagation.


Wired on Mount Athos

Al Jazeera

A crowd of men mills around the port of Ouranoupolis, the so-called City of the Sky and the departure point from which pilgrims and monks enter Mount Athos, the second holiest place in Orthodox Christianity. One of them poses for his selfie-stick against the ageing ship that will convey them along a peninsula studded for a thousand years with 20 monasteries and a tradition of male monasticism. Another downloads the new Mount Athos app on his smartphone to read up on the monasteries he plans to visit and check road connections between them. Others update on Facebook the running online record of their lives, instantly reaping'likes' and peer validation for their pilgrimage. It is a far cry from my first visit to the mountain in 1999, when my father handed me the Diamonitirion, an ecclesiastical visa stamped with the Byzantine two-headed eagle granting four days of access to this medieval monastic state.