Related papers: Entailment in Probability of Thresholded Generaliz…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
We consider a set $\mbK = \bigcup_{n \in \mbbN}\mbK_n$ of {\em finite} structures such that all members of $\mbK_n$ have the same universe, the cardinality of which approaches $\infty$ as $n\to\infty$. Each structure in $\mbK$ may have a…
We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…
There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$,…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
Traditional interpretations of probability, whether frequentist or subjective, make no reference to the concept of energy. In this paper, we propose that assigning hypothetical energy levels to the outcomes of a random variable can yield…
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…
We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the…
In this paper, we present a probabilistic adaptation of an Assume/Guarantee contract formalism. For the sake of generality, we assume that the extended state machines used in the contracts and implementations define sets of runs on a given…
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum-free sets, $B_{h}[g]$-sets and Hilbert cubes. In…
We generalise Ehrhard and Regnier's Taylor expansion from pure to probabilistic $\lambda$-terms through notions of probabilistic resource terms and explicit Taylor expansion. We prove that the Taylor expansion is adequate when seen as a way…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…
Recently maximum pseudo-likelihood (MPL) inference method has been successfully applied to statistical physics models with intractable likelihoods. We use information theory to derive a relation between the pseudo-likelihood and likelihood…
Hyperproperties are properties that describe the correctness of a system as a relation between multiple executions. Hyperproperties generalize trace properties and include information-flow security requirements, like noninterference, as…
Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases,…
This article gives a probabilistic overview of the widely used method of default probability estimation proposed by K. Pluto and D. Tasche. There are listed detailed assumptions and derivation of the inequality where the probability of…