Related papers: Logical reduction of relations: from relational da…

Mechanical proofs by logical relations often involve tedious reasoning about substitution. In this paper, we show that this is not necessarily the case, by developing, in Agda, a proof that all simply typed lambda calculus expressions…

We propose unifying techniques from probabilistic databases and relational embedding models with the goal of performing complex queries on incomplete and uncertain data. We formalize a probabilistic database model with respect to which all…

Systematic comparison of methods for relation extraction (RE) is difficult because many experiments in the field are not described precisely enough to be completely reproducible and many papers fail to report ablation studies that would…

We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.

Learning relations based on evidence from knowledge bases relies on processing the available relation instances. Many relations, however, have clear domain and range, which we hypothesize could help learn a better, more generalizing, model.…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any…

This paper, the first step to connect relational databases with systems consequence (Kent: "System Consequence" 2009), is concerned with the semantics of relational databases. It aims to to study system consequence in the logical/semantic…

Let (L;C) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L;C), i.e., the structures with domain L that are first-order definable in (L;C). We show that up…

We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…

We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining "toric" roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more…

Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types.…

The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…

Several general properties, concerning reduction algebras - rings of definition and algorithmic efficiency of the set of ordering relations - are discussed. For the reduction algebras, related to the diagonal embedding of the Lie algebra…

We reduce phrase-representation parsing to dependency parsing. Our reduction is grounded on a new intermediate representation, "head-ordered dependency trees", shown to be isomorphic to constituent trees. By encoding order information in…

We contribute to a recent research program which aims at revisiting the study of the complexity of word problems, a major area of research in combinatorial algebra, through the lens of the theory of computably enumerable equivalence…

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…

Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without…

The relationship according to which one physical theory encompasses the domain of empirical validity of another is widely known as "reduction." Here it is argued that one popular methodology for showing that one theory reduces to another,…

Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…