Related papers: Foundations for conditional probability
We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by…
We develop a new formalism for constructing probabilities associated to the causal ordering of events in quantum theory, where by an event we mean the emergence of a measurement record on a detector. We start with constructing probabilities…
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability…
Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition…
A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…