Related papers: Learning First-Order Definitions of Functions

We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…

Reflecting our experiences in areas, like Algebraic Specifications, Abstract Model Theory, Graph Transformations, and Model Driven Software Engineering (MDSE), we present a general, category independent approach to Logics of First-Order…

The problem of relevance ranking consists of sorting a set of objects with respect to a given criterion. Since users may prefer different relevance criteria, the ranking algorithms should be adaptable to the user needs. Two main approaches…

First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…

This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…

First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…

The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…

While federated learning traditionally aims to train a single global model across decentralized local datasets, one model may not always be ideal for all participating clients. Here we propose an alternative, where each client only…

Prior work on generating explanations in a planning and decision-making context has focused on providing the rationale behind an AI agent's decision making. While these methods provide the right explanations from the explainer's…

Machine learning is usually defined in behaviourist terms, where external validation is the primary mechanism of learning. In this paper, I argue for a more holistic interpretation in which finding more probable, efficient and abstract…

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking…

The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on sets. We develop the syntax, semantics and…

Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…

In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from…

Recent work in learning ontologies (hierarchical and partially-ordered structures) has leveraged the intrinsic geometry of spaces of learned representations to make predictions that automatically obey complex structural constraints. We…

For a system to understand natural language, it needs to be able to take natural language text and answer questions given in natural language with respect to that text; it also needs to be able to follow instructions given in natural…

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…

The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…

Lin and Zhaos theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the…