Related papers: On A Theory of Probabilistic Deductive Databases
Decomposing predictive uncertainty into epistemic (model ignorance) and aleatoric (data ambiguity) components is central to reliable decision making, yet most methods estimate both from the same predictive distribution. Recent empirical and…
Belnap-Dunn logic (BD), sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two…
We present a formulation of the problem of probabilistic model checking as one of query evaluation over probabilistic logic programs. To the best of our knowledge, our formulation is the first of its kind, and it covers a rich class of…
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…
Large knowledge bases (KBs) are useful in many tasks, but it is unclear how to integrate this sort of knowledge into "deep" gradient-based learning systems. To address this problem, we describe a probabilistic deductive database, called…
A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge.…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
Probabilistic programming is a rapidly developing programming paradigm which enables the formulation of Bayesian models as programs and the automation of posterior inference. It facilitates the development of models and conducting Bayesian…
With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
The necessity to manage inconsistency in Description Logics Knowledge Bases (KBs) has come to the fore with the increasing importance gained by the Semantic Web, where information comes from different sources that constantly change their…
Although pretrained language models (PTLMs) contain significant amounts of world knowledge, they can still produce inconsistent answers to questions when probed, even after specialized training. As a result, it can be hard to identify what…
As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…
Discrete probabilistic programs (DPPs) provide a highly expressive formalism for compactly defining arbitrary finite probabilistic models. This expressivity comes at a price: DPP inference is PSPACE-hard. In this work, we show that DPP…
Learning how to predict future events from patterns of past events is difficult when the set of possible event types is large. Training an unrestricted neural model might overfit to spurious patterns. To exploit domain-specific knowledge of…
Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we introduce…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Large language models (LLMs) are increasingly used in applications requiring factual accuracy, yet their outputs often contain hallucinated responses. While fact-checking can mitigate these errors, existing methods typically retrieve…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
We study here fundamental issues involved in top-k query evaluation in probabilistic databases. We consider simple probabilistic databases in which probabilities are associated with individual tuples, and general probabilistic databases in…