Related papers: Checking Trustworthiness of Probabilistic Computat…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
Transformers have recently been shown to be capable of reliably performing logical reasoning over facts and rules expressed in natural language, but abductive reasoning - inference to the best explanation of an unexpected observation - has…
Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental…
This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the…
A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We…
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…
The role of uncertainty in data management has become more prominent than ever before, especially because of the growing importance of machine learning-driven applications that produce large uncertain databases. A well-known approach to…
Distributed protocols are generally parametric and can be executed on a system with any number of nodes, and hence proving their correctness becomes an infinite state verification problem. The most popular approach for verifying distributed…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…
Due to the black box nature of deep neural networks (DNN), the continuous validation of DNN during operation is challenging with the absence of a human monitor. As a result this makes it difficult for developers and regulators to gain…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
Design verification is a complex and costly task, especially for large and intricate processor projects. Formal verification techniques provide advantages by thoroughly examining design behaviors, but they require extensive labor and…
The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state- a…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
We present a new approach to the type inference problem for dynamic languages. Our goal is to combine \emph{logical} constraints, that is, deterministic information from a type system, with \emph{natural} constraints, that is, uncertain…
Modern cloud-based AI training relies on extensive telemetry and logs to ensure accountability. While these audit trails enable retrospective inspection, they struggle to address the inherent non-determinism of deep learning. Stochastic…
Trusting machine learning algorithms requires having confidence in their outputs. Confidence is typically interpreted in terms of model reliability, where a model is reliable if it produces a high proportion of correct outputs. However,…
We propose an abductive diagnosis theory that integrates probabilistic, causal and taxonomic knowledge. Probabilistic knowledge allows us to select the most likely explanation; causal knowledge allows us to make reasonable independence…