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Knowledge can be represented compactly in a multitude ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a…
Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
We present EntropyDB, an interactive data exploration system that uses a probabilistic approach to generate a small, query-able summary of a dataset. Departing from traditional summarization techniques, we use the Principle of Maximum…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…
Trustworthy artificial intelligence increasingly relies on probabilistic computation to achieve robustness, interpretability, security and privacy. In practical systems, such workloads interleave deterministic data access with repeated…
In this paper, building on work done on measuring inconsistency in knowledge bases, we introduce inconsistency measures for databases. In particular, focusing on databases with denial constraints, we first consider the natural approach of…
Partially observable Markov decision processes (POMDPs) are a fundamental model for sequential decision-making under uncertainty. However, many verification and synthesis problems for POMDPs are undecidable or intractable. Most prominently,…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
A pair of lower and upper cumulative distribution functions, also called probability box or p-box, is among the most popular models used in imprecise probability theory. They arise naturally in expert elicitation, for instance in cases…
Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers and can be used to easily parameterize a rich variety of probability…
In Approval-Based Committee (ABC) voting, each voter lists the candidates they approve and then a voting rule aggregates the individual approvals into a committee that represents the collective choice of the voters. An extensively studied…
Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated
In this paper we present the probabilistic typed natural deduction calculus TPTND, designed to reason about and derive trustworthiness properties of probabilistic computational processes, like those underlying current AI applications.…
We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the…
Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot…
Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic…
Irreducible frequent patters (IFPs) are introduced for transactional databases. An IFP is such a frequent pattern (FP),(x1,x2,...xn), the probability of which, P(x1,x2,...xn), cannot be represented as a product of the probabilities of two…