Related papers: Writing Positive/Negative-Conditional Equations Co…

Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…

For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models…

Standard meta-learning for representation learning aims to find a common representation to be shared across multiple tasks. The effectiveness of these methods is often limited when the nuances of the tasks' distribution cannot be captured…

We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…

We describe an approach to learn, in a term-rewriting setting, function definitions from input/output equations. By confining ourselves to structurally recursive definitions we obtain a fairly fast learning algorithm that often yields…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears…

We study reductions well suited to compare structures and classes of structures with respect to properties based on enumeration reducibility. We introduce the notion of a positive enumerable functor and study the relationship with…

We build a dual-way neural dictionary to retrieve words given definitions, and produce definitions for queried words. The model learns the two tasks simultaneously and handles unknown words via embeddings. It casts a word or a definition to…

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…

In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…

We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…

We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. We then exploit this result…

We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…

This report presents an elementary theory of unification for positive conjunctive queries. A positive conjunctive query is a formula constructed from propositional constants, equations and atoms using the conjunction $\wedge$ and the…

Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…

This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…

Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…