Related papers: Attribute Dependencies for Data with Grades

Fuzzy rule-based systems have been mostly used in interpretable decision-making because of their interpretable linguistic rules. However, interpretability requires both sensible linguistic partitions and small rule-base sizes, which are not…

Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…

The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C") that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound…

Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking…

We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…

In the intricate field of medical diagnostics, capturing the subtle manifestations of diseases remains a challenge. Traditional methods, often binary in nature, may not encapsulate the nuanced variances that exist in real-world clinical…

This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of…

Despite alarm over the reliance of machine learning systems on so-called spurious patterns, the term lacks coherent meaning in standard statistical frameworks. However, the language of causality offers clarity: spurious associations are due…

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of "category" for which equality…

This paper studies how violations of structural assumptions like expected utility and exponential discounting can be connected to basic rationality violations, even though these assumptions are typically regarded as independent building…

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…

We study local consequence relations in modal extensions of product logic over Kripke models with either valued (fuzzy) or crisp accessibility relations. In both settings, we consider semantics over the full class of product algebras as…

Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…

To preserve access to digital content, we must preserve the representation information that captures the intended interpretation of the data. In particular, we must be able to capture performance dependency requirements, i.e. to identify…

Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…

A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…

Since their introduction, fuzzy sets and systems have become an important area of research known for its versatility in modelling, knowledge representation and reasoning, and increasingly its potential within the context explainable AI.…

Most traditional models of uncertainty have focused on the associational relationship among variables as captured by conditional dependence. In order to successfully manage intelligent systems for decision making, however, we must be able…