Related papers: Entailment in Probability of Thresholded Generaliz…
In physics, entanglement 'reduces' the entropy of an entity, because the (von Neumann) entropy of, e.g., a composite bipartite entity in a pure entangled state is systematically lower than the entropy of the component sub-entities. We show…
There are two main approach to probability, one of set-theoretic character where probability is the measure of a set, and another one of linguistic character where probability is the degree of confidence in a proposition. In this work we…
The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being spacelike and timelike, can they still be entangled? If so, how does…
Probability is distinguished into two kinds: physical and epistemic, also, but less accurately, called objective and subjective. Simple postulates are given for physical probability, the only novel one being a locality condition. Translated…
A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
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…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
Different analytic notions of contextuality fall into two major groups: probabilistic and strong notions of contextuality. Kochen and Specker's Theorem~0 is a demarcation criterion for differentiating between those groups. Whereas…
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum…
In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…
We extend a result of Lyons (2016) from fractional tiling of finite graphs to a version for infinite random graphs. The most general result is as follows. Let $\bf P$ be a unimodular probability measure on rooted networks $(G, o)$ with…
For a projective measurement, the Born rule provides the probability for an outcome in terms of the inner product between a projector and a quantum state. If the projector represents a pure entangled state and the state for a composite…
The framework of generalized probabilistic theories (GPTs) is a popular approach for studying the physical foundations of quantum theory. The standard framework assumes the no-restriction hypothesis, in which the state space of a physical…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
Probabilistic word embeddings have shown effectiveness in capturing notions of generality and entailment, but there is very little work on doing the analogous type of investigation for sentences. In this paper we define probabilistic models…