Related papers: Boolean algebras of conditionals, probability and …
We give an overview and conceptual discussion of some of our results on contextuality and non-locality. We focus in particular on connections with the work of Itamar Pitowsky on correlation polytopes, Bell inequalities, and Boole's…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
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…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of…
We give an axiomatic formulation of quantum structures like semilogics and quasilogics which generalize the boolean semirings of events and fuzzy logics. The notions of distributions, states, representations observables and semiobservables…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way…
We study finite probability theory through a category of finite probability schemes and probability-preserving maps, called \emph{bundles}. A bundle simultaneously records a quotient of a sample space, an algebra of random variables, and…
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…
We develop a theory of formal multivariate polynomials over commutative rings by treating them as ring terms. Our main result is that two ring terms are s-equivalent (when expanded they yield the same standard polynomial) iff they are…
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...",…
The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be…
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,…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…