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Domain-general model-based planners often derive their generality by constructing search heuristics through the relaxation or abstraction of symbolic world models. We illustrate how abstract interpretation can serve as a unifying framework…

Artificial Intelligence · Computer Science 2022-08-08 Tan Zhi-Xuan , Joshua B. Tenenbaum , Vikash K. Mansinghka

We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given…

Mathematical Physics · Physics 2018-04-04 Fabio Bagarello , Evaldo M. F. Curado , Jean-Pierre Gazeau

We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little sieve amenability, and conclude that these sets cannot be…

Number Theory · Mathematics 2013-09-04 Christian Elsholtz , Adam J. Harper

Let $\mathcal{P}$ be a set of points in the plane, and $\mathcal{S}$ a strictly convex set of points. In this note, we show that if $\mathcal{P}$ contains many translates of $\mathcal{S}$, then these translates must come from a generalized…

Combinatorics · Mathematics 2023-02-28 Gabriel Currier , Jozsef Solymosi , Ethan Patrick White

This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FLe-algebras). In particular,…

Logic · Mathematics 2024-11-20 Davide Fazio , Gavin St. John

We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics. We propose generalized BI algebras (GBI-algebras) as a common framework…

Logic in Computer Science · Computer Science 2018-09-27 Peter Jipsen , Tadeusz Litak

We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…

Logic · Mathematics 2025-08-06 Célia Borlido , Ganna Kudryavtseva , Brett McLean

In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which…

Artificial Intelligence · Computer Science 2025-05-01 Kenneth Skiba , Tjitze Rienstra , Matthias Thimm , Jesse Heyninck , Gabriele Kern-Isberner

This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with…

Logic in Computer Science · Computer Science 2023-07-12 Carlo Proietti , Fernando R. Velázquez-Quesada , Antonio Yuste-Ginel

The present paper extends generalized morphisms of relations into the realm of Monoidal Fuzzy Logics by first proving and then using relational inequalities over pseudo-associative BK-products (compositions) of relations in these logics. In…

Logic · Mathematics 2009-09-29 Ladislav J. Kohout

This is in some sense an addendum to the book Relational Mathematics by the first-named author. It originated from work on diverse other topics during which a lot of purely relational results with broad applicability have been produced.…

Discrete Mathematics · Computer Science 2014-03-28 Gunther Schmidt , Michael Winter

In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable…

Logic · Mathematics 2023-01-24 Ivan Chajda , Davide Fazio , Helmut Länger , Antonio Ledda , Jan Paseka

In this paper, we compose a new task for deep argumentative structure analysis that goes beyond shallow discourse structure analysis. The idea is that argumentative relations can reasonably be represented with a small set of predefined…

Computation and Language · Computer Science 2017-12-08 Paul Reisert , Naoya Inoue , Naoaki Okazaki , Kentaro Inui

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…

Programming Languages · Computer Science 2022-07-05 Fritz Henglein , Robin Kaarsgaard , Mikkel Kragh Mathiesen

Within the categorical compositional distributional model of meaning, we provide semantic interpretations for the subject and object roles of the possessive relative pronoun `whose'. This is done in terms of Frobenius algebras over compact…

Computation and Language · Computer Science 2014-06-19 Mehrnoosh Sadrzadeh , Stephen Clark , Bob Coecke

A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational…

Logic · Mathematics 2022-07-25 Prosenjit Howlader , Mohua Banerjee

Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…

Category Theory · Mathematics 2024-12-31 Benedikt Ahrens , Peter LeFanu Lumsdaine , Paige Randall North

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…

Logic in Computer Science · Computer Science 2023-10-20 Alexander V. Gheorghiu , David J. Pym

The A-model for finite rank singular perturbations of class $\mathfrak{H}_{-m-2}\smallsetminus\mathfrak{H}_{-m-1}$, $m\in\mathbb{N}$, is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces…

Functional Analysis · Mathematics 2020-08-03 Rytis Jursenas

This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…

Formal Languages and Automata Theory · Computer Science 2024-07-04 Rafał Stefański