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Related papers: Term satisfiability in FL$_\mathrm{ew}$-algebras

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We propose a calculus of string diagrams to reason about satisfiability of Boolean formulas, and prove it to be sound and complete. We then showcase our calculus in a few case studies. First, we consider SAT-solving. Second, we consider…

Logic in Computer Science · Computer Science 2023-06-22 Tao Gu , Robin Piedeleu , Fabio Zanasi

Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…

High Energy Physics - Theory · Physics 2026-02-11 Thomas W. Grimm , David Prieto , Mick van Vliet

The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…

Logic in Computer Science · Computer Science 2023-06-22 Francesco Ciraulo , Michele Contente

We prove a strong conceptual completeness theorem (in the sense of Makkai) for the infinitary logic $\mathcal L_{\omega_1\omega}$: every countable $\mathcal L_{\omega_1\omega}$-theory can be canonically recovered from its standard Borel…

Logic · Mathematics 2019-08-06 Ruiyuan Chen

Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…

Logic in Computer Science · Computer Science 2021-12-10 Oliver Nash

We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted $\R\times \R$-graded full field algebra is equivalent to an algebra over a partial operad constructed…

Quantum Algebra · Mathematics 2011-04-11 Liang Kong

Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for \emph{approximate} amenability have been open for some years now. In this article we give a complete…

Functional Analysis · Mathematics 2011-04-11 Yemon Choi , Fereidoun Ghahramani

We relate duality mappings to the "Babbage equation" F(F(z)) = z, with F a map linking weak- to strong-coupling theories. Under fairly general conditions F may only be a specific conformal transformation of the fractional linear type. This…

Statistical Mechanics · Physics 2015-01-08 Zohar Nussinov , Gerardo Ortiz , Mohammad-Sadegh Vaezi

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

Rings and Algebras · Mathematics 2017-08-04 Nathan BeDell

We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…

Logic · Mathematics 2026-01-21 Meng-Che "Turbo" Ho , Martin Ritter , Luca San Mauro

We review and develop the general properties of $L_\infty$ algebras focusing on the gauge structure of the associated field theories. Motivated by the $L_\infty$ homotopy Lie algebra of closed string field theory and the work of Roytenberg…

High Energy Physics - Theory · Physics 2017-04-26 Olaf Hohm , Barton Zwiebach

We introduce hybrid algebras as algebraic semantics for hybrid languages with nominals and, possibly, the satisfaction operator. We establish a duality between hybrid algebras and the descriptive two-sorted general frames of Ten Cate. We…

Logic · Mathematics 2016-04-26 Willem Conradie , Claudette Robinson

Let $G$ be a locally compact group. We show that its Fourier algebra $A(G)$ is amenable if and only if $G$ has an abelian subgroup of finite index, and that its Fourier-Stieltjes algebra $B(G)$ is amenable if and only if $G$ has a compact,…

Functional Analysis · Mathematics 2007-05-23 Brian E. Forrest , Volker Runde

Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…

Quantum Physics · Physics 2016-11-28 Alexander V Turbiner

We define a class of algebras, the semilattices of Mal'cev blocks (for short, SMB algebras). In a nutshell, these algebras are semilattices in which each element gets blown up into a Mal'cev algebra. We publish for the first time our old…

Computational Complexity · Computer Science 2026-04-08 Petar Marković , Miklós Maróti , Ralph McKenzie , Aleksandar Prokić

Building on \'Esik and Kuich's completeness result for finitely weighted Kleene algebra, we establish relational and language completeness results for finitely weighted Kleene algebra with tests. Similarly as \'Esik and Kuich, we assume…

Logic in Computer Science · Computer Science 2024-07-11 Igor Sedlár

All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…

Logic · Mathematics 2023-10-04 Nikolaos Galatos , Gavin St. John

The notion of Fr\'{e}chet locally $C^*$-algebra generalizes the notion of $C^*$-algebra. In this paper, we first present some definitions and basic facts about locally $C^*$-algebra, and then we introduce and study the notion of ideal and…

Operator Algebras · Mathematics 2021-12-17 Ali Rejali , Ali Ranjbari

We provide a general description of realisations of W--algebras in terms of smaller W--algebras and free fields. This is based on the definition of the W--algebra as the commutant of a set of screening charges. This is conjectured to be…

High Energy Physics - Theory · Physics 2009-10-22 G. M. T. Watts

We study the satisfiability problem for the fluted fragment extended with transitive relations. The logic enjoys the finite model property when only one transitive relation is available and the finite model property is lost when…

Logic in Computer Science · Computer Science 2024-05-22 Ian Pratt-Hartmann , Lidia Tendera
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