Related papers: Quantifying knowledge with a new calculus for beli…
A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…
Developing a general information processing model in uncertain environments is fundamental for the advancement of explainable artificial intelligence. Dempster-Shafer theory of evidence is a well-known and effective reasoning method for…
Kolmogorov's foundation of probability takes measure spaces, $\sigma$-algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framework is inadequate for random phenomena involving quantum…
In this paper, we describe a scheme for propagating belief functions in certain kinds of trees using only local computations. This scheme generalizes the computational scheme proposed by Shafer and Logan1 for diagnostic trees of the type…
When reasoning with uncertainty there are many situations where evidences are not only uncertain but their propositions may also be weakly specified in the sense that it may not be certain to which event a proposition is referring. It is…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
The belief function approach to uncertainty quantification as proposed in the Demspter-Shafer theory of evidence is established upon the general mathematical models for set-valued observations, called random sets. Set-valued predictions are…
This paper is concerned with the apparent greatest weakness of the Mathematical Theory of Evidence (MTE) of Shafer \cite{Shafer:76}, which has been strongly criticized by Wasserman \cite{Wasserman:92ijar}. Weaknesses of Shafer's proposal…
We formulate Dempster Shafer Belief functions in terms of Propositional Logic using the implicit notion of provability underlying Dempster Shafer Theory. Given a set of propositional clauses, assigning weights to certain propositional…
In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…
Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and…
Shafer's theory of belief and the Bayesian theory of probability are two alternative and mutually inconsistent approaches toward modelling uncertainty in artificial intelligence. To help reduce the conflict between these two approaches,…
Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through…
In the current versions of the Dempster-Shafer theory, the only essential restriction on the validity of the rule of combination is that the sources of evidence must be statistically independent. Under this assumption, it is permissible to…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
To develop an approach to utilizing continuous statistical information within the Dempster- Shafer framework, we combine methods proposed by Strat and by Shafero We first derive continuous possibility and mass functions from…
A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…
The fundamental updating process in the transferable belief model is related to the concept of specialization and can be described by a specialization matrix. The degree of belief in the truth of a proposition is a degree of justified…
The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…