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The Calculus of Conjunctive Queries (CCQ) has foundational status in database theory. A celebrated theorem of Chandra and Merlin states that CCQ query inclusion is decidable. Its proof transforms logical formulas to graphs: each query has a…
Classical approaches for OLAP assume that the data of all tables is complete. However, in case of incomplete tables with missing tuples, classical approaches fail since the result of a SQL aggregate query might significantly differ from the…
This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…
The success of SQL, NoSQL, and NewSQL databases is a reflection of their ability to provide significant functionality and performance benefits for specific domains, such as financial transactions, internet search, and data analysis. The…
There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…
Large Language Models (LLMs) have made significant progress in assisting users to query databases in natural language. While LLM-based techniques provide state-of-the-art results on many standard benchmarks, their performance significantly…
Without any doubt, the relational paradigm has been a huge success. At the same time, we believe that the time is ripe to rethink how database systems could look like if we designed them from scratch. Would we really end up with the same…
Graph query languages feature mainly two kinds of queries when applied to a graph database: those inspired by relational databases which return tables such as SELECT queries and those which return graphs such as CONSTRUCT queries in SPARQL.…
A correspondence between database tuples as causes for query answers in databases and tuple-based repairs of inconsistent databases with respect to denial constraints has already been established. In this work, answer-set programs that…
The Shapley value is a conventional and well-studied function for determining the contribution of a player to the coalition in a cooperative game. Among its applications in a plethora of domains, it has recently been proposed to use the…
We study the logic of comparative concept similarity $\CSL$ introduced by Sheremet, Tishkovsky, Wolter and Zakharyaschev to capture a form of qualitative similarity comparison. In this logic we can formulate assertions of the form " objects…
We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations have an index -- and explore the consequences of adding the…
Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…
Database system is an indispensable part of software projects. It plays an important role in data organization and storage. Its performance and efficiency are directly related to the performance of software. Nowadays, we have many general…
Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be…
The notion of actual causation, as formalized by Halpern and Pearl, has been recently applied to relational databases, to characterize and compute actual causes for possibly unexpected answers to monotone queries. Causes take the form of…
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…
We present a general relational semantics framework which, by varying the axiomatization and components of the relational structures, provides a uniform semantics for sentential logics, classical and non-classical alike. The approach we…
Closed classes of three-valued logic generated by periodic symmetric funtions that equal $1$ in tuples from $\{1,2\}^n$ and equal $0$ on the rest tuples are considered. Criteria for bases existence and finite bases existence for these…
This paper concerns the paraconsistent logic LPQ$^{\supset,\mathsf{F}}$ and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a consistent…