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A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…

Rings and Algebras · Mathematics 2024-11-20 Peter F. Faul , Amartya Goswami , Gideo Joubert , Graham Manuell

Probabilistic databases (PDBs) model uncertainty in data. The current standard is to view PDBs as finite probability spaces over relational database instances. Since many attributes in typical databases have infinite domains, such as…

Databases · Computer Science 2022-06-01 Martin Grohe , Peter Lindner

We study the complexity of evaluating queries on probabilistic databases under bag semantics. We focus on self-join free conjunctive queries, and probabilistic databases where occurrences of different facts are independent, which is the…

Databases · Computer Science 2023-07-18 Martin Grohe , Peter Lindner , Christoph Standke

The implication problem for conditional independence (CI) asks whether the fact that a probability distribution obeys a given finite set of CI relations implies that a further CI statement also holds in this distribution. This problem has a…

Statistics Theory · Mathematics 2024-04-25 Mathias Drton , Leonard Henckel , Benjamin Hollering , Pratik Misra

A new characterization is given to describe implication bases of a closure system in terms of the system's quasi-closed sets. Using this characterization, it is possible to show that groups of implications corresponding to distinct…

Logic · Mathematics 2023-05-30 Todd Bichoupan

The report suggests the concept of risk, outlining two mathematical structures necessary for risk genesis: the set of outcomes and, in a general case, partial order of preference on it. It is shown that this minimum partial order should…

Artificial Intelligence · Computer Science 2020-04-14 Tatiana Urazaeva

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…

Logic in Computer Science · Computer Science 2024-03-29 Alexandru Baltag , Johan van Benthem , Dazhu Li

We study the problem of entity-relation extraction in the presence of symbolic domain knowledge. Such knowledge takes the form of an ontology defining relations and their permissible arguments. Previous approaches set out to integrate such…

Machine Learning · Computer Science 2021-03-23 Kareem Ahmed , Eric Wang , Guy Van den Broeck , Kai-Wei Chang

With the increasing demand of intelligent systems capable of operating in different contexts (e.g. users on the move) the correct interpretation of the user-need by such systems has become crucial to give consistent answers to the user…

Computation and Language · Computer Science 2023-12-18 Lorenzo Massai

During the last decade, entity embeddings have become ubiquitous in Artificial Intelligence. Such embeddings essentially serve as compact but semantically meaningful representations of the entities of interest. In most approaches, vectors…

Artificial Intelligence · Computer Science 2021-09-15 Steven Schockaert

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…

Machine Learning · Computer Science 2013-01-07 Ben Taskar , Pieter Abbeel , Daphne Koller

Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…

Programming Languages · Computer Science 2025-01-31 Joseph Eremondi , Ohad Kammar

Codd's Theorem, a fundamental result of database theory, asserts that relational algebra and relational calculus have the same expressive power on relational databases. We explore Codd's Theorem for databases over semirings and establish…

Logic in Computer Science · Computer Science 2025-04-16 Guillermo Badia , Phokion G. Kolaitis , Carles Noguera

The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…

Logic · Mathematics 2018-04-09 A Mani

We investigate the effect of various dependency-based word embeddings on distinguishing between functional and domain similarity, word similarity rankings, and two downstream tasks in English. Variations include word embeddings trained…

Computation and Language · Computer Science 2018-04-18 Sean MacAvaney , Amir Zeldes

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss…

Statistics Theory · Mathematics 2016-07-25 Edward H. Kennedy

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…

Machine Learning · Statistics 2020-09-04 Aditya Kela , Kai von Prillwitz , Johan Aberg , Rafael Chaves , David Gross

Microservices have been a key architectural approach for over a decade, transforming system design by promoting decentralization and allowing development teams to work independently on specific microservices. While loosely coupled…

Software Engineering · Computer Science 2025-01-22 Amr S. Abdelfattah , Kari E Cordes , Austin Medina , Tomas Cerny

Querying is one of the basic functionality expected from a database system. Query efficiency is adversely affected by increase in the number of participating tables. Also, querying based on syntax largely limits the gamut of queries a…

Databases · Computer Science 2011-04-08 Gowri Shankar Ramaswamy , F Sagayaraj Francis

We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree,…

Logic · Mathematics 2024-08-23 Paolo Baldi , Esther Anna Corsi , Hykel Hosni