Algebraic Reasoning over Relational Structures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139638" target="_blank" >RIV/00216224:14310/24:00139638 - isvavai.cz</a>

Výsledek na webu

<a href="https://entics.episciences.org/14598" target="_blank" >https://entics.episciences.org/14598</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.46298/entics.14598" target="_blank" >10.46298/entics.14598</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Algebraic Reasoning over Relational Structures

Popis výsledku v původním jazyce

Many important computational structures involve an intricate interplay between algebraic features (given by operations on the underlying set) and relational features (taking account of notions such as order or distance). This paper investigates algebras over relational structures axiomatized by an infinitary Horn theory, which subsume, for example, partial algebras, various incarnations of ordered algebras, quantitative algebras introduced by Mardare, Panangaden, and Plotkin, and their recent extension to generalized metric spaces and lifted algebraic signatures by Mio, Sarkis, and Vignudelli. To this end, we develop the notion of clustered equation, which is inspired by Mardare et al.'s basic conditional equations in the theory of quantitative algebras, at the level of generality of arbitrary relational structures, and we prove that it is equivalent to an abstract categorical form of equation earlier introduced by Milius and Urbat. Our main results are a family of Birkhoff-type variety theorems (classifying the expressive power of clustered equations) and an exactness theorem (classifying abstract equations by a congruence property).

Název v anglickém jazyce

Algebraic Reasoning over Relational Structures

Popis výsledku anglicky

Many important computational structures involve an intricate interplay between algebraic features (given by operations on the underlying set) and relational features (taking account of notions such as order or distance). This paper investigates algebras over relational structures axiomatized by an infinitary Horn theory, which subsume, for example, partial algebras, various incarnations of ordered algebras, quantitative algebras introduced by Mardare, Panangaden, and Plotkin, and their recent extension to generalized metric spaces and lifted algebraic signatures by Mio, Sarkis, and Vignudelli. To this end, we develop the notion of clustered equation, which is inspired by Mardare et al.'s basic conditional equations in the theory of quantitative algebras, at the level of generality of arbitrary relational structures, and we prove that it is equivalent to an abstract categorical form of equation earlier introduced by Milius and Urbat. Our main results are a family of Birkhoff-type variety theorems (classifying the expressive power of clustered equations) and an exactness theorem (classifying abstract equations by a congruence property).

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/GA22-02964S" target="_blank" >GA22-02964S: Obohacené kategorie a jejich aplikace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the Fortieth Conference on the Mathematical Foundations of Programming Semantics, Volume 4

ISBN

—

ISSN

2969-2431

e-ISSN

2969-2431

Počet stran výsledku

20

Strana od-do

„13-1“-„13-20“

Název nakladatele

Inria

Místo vydání

France

Místo konání akce

Oxford

Datum konání akce

19. 6. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—