相关论文: Probabilistic Events and Physical Reality: A Compl…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
This paper considers the notion of possible events which are insignificant in probabilistic analysis (i.e. events that have zero probability). The paper discusses the method of modal logic based on "possible worlds" and discusses a…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…
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…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
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…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…