Related papers: Counting Answers to Existential Positive Queries: …
The complexity class $\exists\mathbb R$, standing for the complexity of deciding the existential first order theory of the reals as real closed field in the Turing model, has raised considerable interest in recent years. It is well known…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…
A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the…
Distributional compositional (DisCo) models are functors that compute the meaning of a sentence from the meaning of its words. We show that DisCo models in the category of sets and relations correspond precisely to relational databases. As…
We prove The Equivalence Theorem: structurally complete knowledge representation requires exactly four mutually entailing capabilities -- n-ary relationships with attributes, temporal validity, uncertainty quantification, and causal…
On a finite structure, the polymorphism invariant relations are exactly the primitively positively definable relations. On infinite structures, these two sets of relations are different in general. Infinitary primitively positively…
We provide a wide-ranging study of the scenario where a subset of the relations in a relational vocabulary are visible to a user --- that is, their complete contents are known --- while the remaining relations are invisible. We also have a…
Given the emergent reasoning abilities of large language models, information retrieval is becoming more complex. Rather than just retrieve a document, modern information retrieval systems advertise that they can synthesize an answer based…
We perform a fundamental investigation of the complexity of conjunctive query evaluation from the perspective of parameterized complexity. We classify sets of boolean conjunctive queries according to the complexity of this problem. Previous…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
We study query answering in the description logic $\mathcal{SQ}$ supporting qualified number restrictions on both transitive and non-transitive roles. Our main contributions are a tree-like model property for $\mathcal{SQ}$ knowledge bases…
Database theory is exciting because it studies highly general and practically useful abstractions. Conjunctive query (CQ) evaluation is a prime example: it simultaneously generalizes graph pattern matching, constraint satisfaction, and…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
Consider the situation where a query is to be answered using Web sources that restrict the accesses that can be made on backend relational data by requiring some attributes to be given as input of the service. The accesses provide lookups…
Queries with aggregation and arithmetic operations, as well as incomplete data, are common in real-world database, but we lack a good understanding of how they should interact. On the one hand, systems based on SQL provide ad-hoc rules for…
In ontology-based data access (OBDA), the classical database is enhanced with an ontology in the form of logical assertions generating new intensional knowledge. A powerful form of such logical assertions is the tuple-generating…
We prove that, on bounded expansion classes, every first-order formula with modulo counting is equivalent, in a linear-time computable monadic expansion, to an existential first-order formula. As a consequence, we derive, on bounded…
Thanks to information extraction and semantic Web efforts, search on unstructured text is increasingly refined using semantic annotations and structured knowledge bases. However, most users cannot become familiar with the schema of…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…