Related papers: Set-Theoretic Preliminaries for Computer Scientist…
The fundamentals of formal logic, theory of sets and mathematical structures are narrated in terms of relations language.
The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a…
Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…
The handling of user preferences is becoming an increasingly important issue in present-day information systems. Among others, preferences are used for information filtering and extraction to reduce the volume of data presented to the user.…
Inducing association rules is one of the central tasks in data mining applications. Quantitative association rules induced from databases describe rich and hidden relationships holding within data that can prove useful for various…
We study here preference revision, considering both the monotonic case where the original preferences are preserved and the nonmonotonic case where the new preferences may override the original ones. We use a relational framework in which…
Mathematicians manipulate sets with confidence almost every day, rarely making mistakes. Few of us, however, could accurately quote what are often referred to as "the" axioms of set theory. This suggests that we all carry around with us,…
The task of generating a database query from a question in natural language suffers from ambiguity and insufficiently precise description of the goal. The problem is amplified when the system needs to generalize to databases unseen at…
In this paper, we show how to use a Relational Database Management System in support of Finite Element Analysis. We believe it is a new way of thinking about data management in well-understood applications to prepare them for two major…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
Binary relations are commonly used in Computer Science for modeling data. In addition to classical representations using matrices or lists, some compressed data structures have recently been proposed to represent binary relations in compact…
Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for models with a log-convex likelihood, which are ubiquitous in the…
There are significant benefits to serve deep learning models from relational databases. First, features extracted from databases do not need to be transferred to any decoupled deep learning systems for inferences, and thus the system…
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their…
Posets are discrete mathematical structures which are ubiquitous in a broad range of data analysis and machine learning applications. Research connecting posets to the data science domain has been ongoing for many years. In this paper, a…
Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…
Databases are widespread, yet extracting relevant data can be difficult. Without substantial domain knowledge, multivariate search queries often return sparse or uninformative results. This paper introduces an approach for searching…