Related papers: A Compositional Query Algebra for Second-Order Log…
This paper concerns an expansion of first-order Belnap-Dunn logic, named $\mathrm{BD}^{\supset,\mathsf{F}}$, and an application of this logic in the area of relational database theory. The notion of a relational database, the notion of a…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
In the framework of computable queries in Database Theory, there are many examples of queries to (properties of) relational database instances that can be expressed by simple and elegant third order logic ($\mathrm{TO}$) formulae. In many…
A new seemingly weak axiomatic formulation of information algebras is given. It is shown how such information algebras can be embedded into set (information) algebras. In set algebras there is a natural relation of conditional independence…
This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
Compositional generalization allows efficient learning and human-like inductive biases. Since most research investigating compositional generalization in NLP is done on English, important questions remain underexplored. Do the necessary…
Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and…
The paper analyzes and characterizes the algebraic and logical structure of the multiset semantics for SPARQL patterns involving AND, UNION, FILTER, EXCEPT, and SELECT. To do this, we align SPARQL with two well-established query languages:…
Nested relational query languages have been explored extensively, and underlie industrial language-integrated query systems such as Microsoft's LINQ. However, relational databases do not natively support nested collections in query results.…
Two important aspects of semantic parsing for question answering are the breadth of the knowledge source and the depth of logical compositionality. While existing work trades off one aspect for another, this paper simultaneously makes…
We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the…
In this paper, we propose Multi-Modal Databases (MMDBs), which is a new class of database systems that can seamlessly query text and tables using SQL. To enable seamless querying of textual data using SQL in an MMDB, we propose to extend…
Generating structural query language (SQL) queries from natural language is a long-standing open problem. Answering a natural language question about a database table requires modeling complex interactions between the columns of the table…
Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
We describe some recent approaches to score-based explanations for query answers in databases and outcomes from classification models in machine learning. The focus is on work done by the author and collaborators. Special emphasis is placed…
This paper examines two related problems that are central to developing an autonomous decision-making agent, such as a robot. Both problems require generating structured representafions from a database of unstructured declarative knowledge…