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Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
Embedding-based Knowledge Base Completion models have so far mostly combined distributed representations of individual entities or relations to compute truth scores of missing links. Facts can however also be represented using pairwise…
In this paper a new saturation model is presented. This model is based on the theoretical solution for the generating functional, and it is quite different and not more complicated than the Glauber-like approach used before. The model…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
Equality saturation is a powerful technique for program optimization. Contextual equality saturation extends this to support rewrite rules that are conditioned on where a term appears in an expression. Existing work has brought contextual…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic…
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…
Querying graph databases has recently received much attention. We propose a new approach to this problem, which balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our…
A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…
Recent approaches to verifying programs in separation logics for concurrency have used state transition systems (STSs) to specify the atomic operations of programs. A key challenge in the setting has been to compose such STSs into larger…
In the recent years, a lot of attention has been paid to the development of solid foundations for the composition and inversion of schema mappings. In this paper, we review the proposals for the semantics of these crucial operators. For…
We investigate the problem of aligning two RDF databases, an essential problem in understanding the evolution of ontologies. Our approaches address three fundamental challenges: 1) the use of "blank" (null) names, 2) ontology changes in…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
In this paper we study the problem of reducing the evaluation costs of queries on finite databases in presence of integrity constraints, by designing and materializing views. Given a database schema, a set of queries defined on the schema,…
We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…
Reasoning about functions that operate over algebraic data types is an important problem for a large variety of applications. One application of particular interest is network applications that manipulate or reason about complex message…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic…