Related papers: Relational Algebra and Calculus with SQL Null Valu…
Every database system contains a query optimizer that performs query rewrites. Unfortunately, developing query optimizers remains a highly challenging task. Part of the challenges comes from the intricacies and rich features of query…
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau…
The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on quantification theory by Frege and Peirce himself, paved the…
Although database systems perform well in data access and manipulation, their relational model hinders data scientists from formulating machine learning algorithms in SQL. Nevertheless, we argue that modern database systems perform well for…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
The main purpose of this paper is to define dynamical degrees for rational maps over an algebraic closed field of characteristic zero and prove some basic properties (such as log-concavity) and give some applications. We also define…
Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
Many existing end-to-end systems for hybrid question answering tasks can often be boiled down to a "prompt-and-pray" paradigm, where the user has limited control and insight into the intermediate reasoning steps used to achieve the final…
Text-to-SQL parsing is an essential and challenging task. The goal of text-to-SQL parsing is to convert a natural language (NL) question to its corresponding structured query language (SQL) based on the evidences provided by relational…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
We present a bisequent calculus (BSC) for the minimal theory of definite descriptions (DD) in the setting of neutral free logic, where formulae with non-denoting terms have no truth value. The treatment of quantifiers, atomic formulae and…
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
Functional programming comes in two flavours: one where ``functions are first-class citizens'' (we call this applicative) and one which is based on equations (we call this declarative). In relational programming clauses play the role of…
In this paper we presented the semantics of database mappings in the relational DB category based on the power-view monad T and monadic algebras. The objects in this category are the database-instances (a database-instance is a set of n-ary…
Relation classification aims to extract semantic relations between entity pairs from the sentences. However, most existing methods can only identify seen relation classes that occurred during training. To recognize unseen relations at test…
We present a generative model to map natural language questions into SQL queries. Existing neural network based approaches typically generate a SQL query word-by-word, however, a large portion of the generated results are incorrect or not…