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Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula for the number of representations of an integer as a sum of $k\geq 5$ primes. Our error terms in such a formula improve by some logarithmic factors…
Much of the power of probabilistic methods in modelling language comes from their ability to compare several derivations for the same string in the language. An important starting point for the study of such cross-derivational properties is…
LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic…
We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building Bayesian models of the kinds used in…
In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by…
We present a probabilistic model for constraint-based grammars and a method for estimating the parameters of such models from incomplete, i.e., unparsed data. Whereas methods exist to estimate the parameters of probabilistic context-free…
We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with control structures, such as conditionals and loops. POCKA enables reasoning about programs that can access…
Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different…
Artificial neural networks are a state-of-the-art solution for many problems in natural language processing. What can we learn about language and meaning from the way artificial neural networks represent it? Word representations obtained…
How predictable a word is can be quantified in two ways: using human responses to the cloze task or using probabilities from language models (LMs).When used as predictors of processing effort, LM probabilities outperform probabilities…
We introduce a probabilistic extension of Levy's Call-By-Push-Value. This extension consists simply in adding a " flipping coin " boolean closed atomic expression. This language can be understood as a major generalization of Scott's PCF…
Programs that combine I/O and countable probabilistic choice, modulo either bisimilarity or trace equivalence, can be seen as describing a probabilistic strategy. For well-founded programs, we might expect to axiomatize bisimilarity via a…
We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops. Our method is built on a denotational semantics represented by probability generating…
In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and…
We prove a precise formula for the minimal number K(n) such that every binary word of length $n$ can be divided into K(n) palindromes. Also we estimate the average number $\ol K(n)$ of palindromes composing a random binary word of the…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
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…
We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics,…
We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…
In this work, we study the fully automated inference of expected result values of probabilistic programs in the presence of natural programming constructs such as procedures, local variables and recursion. While crucial, capturing these…