Algebraic Reasoning over Relational Structures

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Algebraic Reasoning over Relational Structures
Original language description
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).
Czech name
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Czech description
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Project
<a href="/en/project/GA22-02964S" target="_blank" >GA22-02964S: Enriched categories and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the Fortieth Conference on the Mathematical Foundations of Programming Semantics, Volume 4
ISBN
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ISSN
2969-2431
e-ISSN
2969-2431
Number of pages
20
Pages from-to
„13-1“-„13-20“
Publisher name
Inria
Place of publication
France
Event location
Oxford
Event date
Jun 19, 2024
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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