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Over twenty years ago, Abadi et al. established the Dependency Core Calculus (DCC) as a general purpose framework for analyzing dependency in typed programming languages. Since then, dependency analysis has shown many practical benefits to…
The problem of checking whether two programs are semantically equivalent or not has a diverse range of applications, and is consequently of substantial importance. There are several techniques that address this problem, chiefly by…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
The chase is a fundamental algorithm with ubiquitous uses in database theory. Given a database and a set of existential rules (aka tuple-generating dependencies), it iteratively extends the database to ensure that the rules are satisfied in…
We present associative and causal views of differential privacy. Under the associative view, the possibility of dependencies between data points precludes a simple statement of differential privacy's guarantee as conditioning upon a single…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
There is a lack of formalism for some key foundational concepts in systems engineering. One of the most recently acknowledged deficits is the inadequacy of systems engineering practices for engineering intelligent systems. In our previous…
Let F be a field complete for a real valuation. It is a standard result in valuation theory that a finite extension of F admits a valuation basis if and only if it is without defect. We show that even otherwise, one can construct bases in…
In this paper, we investigate the parameterized complexity of model checking for Dependence Logic which is a well studied logic in the area of Team Semantics. We start with a list of nine immediate parameterizations for this problem,…
We propose a method to construct a joint statistical model for mixed-domain data to analyze their dependence. Multivariate Gaussian and log-linear models are particular examples of the proposed model. It is shown that the functional…
Inquiries such as whether a task A depends on a task B, whether an author A has been influenced by a paper B, whether a certain protein is associated with a specific biological process or molecular function, or whether class A inherits from…
We propose a formal approach for relating abstract separation logic library specifications with the trace properties they enforce on interactions between a client and a library. Separation logic with abstract predicates enforces a resource…
Association Rules are a basic concept of data mining. They are, however, not understood as logical objects which can be used for reasoning. The purpose of this paper is to investigate a model based semantic for implications with certain…
Dependency analysis is a program analysis that determines potential data flow between program points. While it is not a security analysis per se, it is a viable basis for investigating data integrity, for ensuring confidentiality, and for…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
In practice, there are many dynamic covering decision information systems, and knowledge reduction of dynamic covering decision information systems is a significant challenge of covering-based rough sets. In this paper, we first study…
Universal algebra and clone theory have proven to be a useful tool in the study of constraint satisfaction problems since the complexity, up to logspace reductions, is determined by the set of polymorphisms of the constraint language. For…
This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…
The purpose of this article is to propose and investigate a partial order structure weaker than the lattice structure and which have nice properties regarding closure operators. We extend accordingly closed pattern mining and formal concept…