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Joint extraction of entities and relations from unstructured texts is a crucial task in information extraction. Recent methods achieve considerable performance but still suffer from some inherent limitations, such as redundancy of relation…

In classical analysis, the convergence behavior of power series solutions to differential or recurrence equations is generally assumed to be invariant under internal rearrangement. This paper challenges that belief by proving that, for…

Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…

Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems…

Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…

Different techniques have been used to prove several transference theorems of the form "nontrivial algorithms for a circuit class C yield circuit lower bounds against C". In this survey we revisit many of these results. We discuss how…

The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…

Recently, a proposal has been advanced to detect unconstitutional partisan gerrymandering with a simple formula called the efficiency gap. The efficiency gap is now working its way towards a possible landmark case in the Supreme Court. This…

In Bayesian analysis, reference priors are widely recognized for their objective nature. Yet, they often lead to intractable and improper priors, which complicates their application. Besides, informed prior elicitation methods are penalized…

In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor…

To determine the welfare implications of price changes in demand data, we introduce a revealed preference relation over prices. We show that the absence of cycles in this relation characterizes a consumer who trades off the utility of…

In a previous paper, a tableau calculus has been presented, which constitute a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work extends such a calculus to multi-modal…

For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…

In this paper, we show that the class of representable residuated semigroups has the finite representation property. That is, every finite representable residuated semigroup is representable over a finite base. This result gives a positive…

Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances…

To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…

Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…

The present paper investigates consequence relations that are both non-monotonic and paraconsistent. More precisely, we put the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference…

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…

We use the technique of "classical realizability" to build new models of ZF + DC in which R is not well ordered. This gives new relative consistency results, probably not obtainable by forcing. This gives also a new method to get programs…