Catoids and modal convolution algebras

U Fahrenberg, C Johansen, G Struth, K Ziemiański - Algebra universalis, 2023 - Springer
We show how modal quantales arise as convolution algebras QX of functions from catoids
X, multisemigroups equipped with source and target maps, into modal quantales value or …

Existential calculi of relations with transitive closure: Complexity and edge saturations

Y Nakamura - 2023 38th Annual ACM/IEEE Symposium on …, 2023 - ieeexplore.ieee.org
We study the decidability and complexity of equational theories of the existential calculus of
relations with transitive closure (ECoR*) and its fragments, where ECoR* is the positive …

Automated Engineering of Relational and Algebraic Methods in Isabelle/HOL: (Invited Tutorial)

S Foster, G Struth, T Weber - … and Algebraic Methods in Computer Science …, 2011 - Springer
We present a new integration of relational and algebraic methods in the Isabelle/HOL
theorem proving environment. It consists of a fine grained hierarchy of algebraic structures …

[HTML][HTML] Ordered domain algebras

R Hirsch, S Mikulás - Journal of Applied Logic, 2013 - Elsevier
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[PDF][PDF] Program construction and verification components based on Kleene algebra

VBF Gomes, G Struth - Archive of Formal Proofs, 2016 - isa-afp.org
Variants of Kleene algebra support program construction and verification by algebraic
reasoning. This entry provides a verification component for Hoare logic based on Kleene …

Axiomatizability of representable domain algebras

R Hirsch, S Mikulás - The Journal of Logic and Algebraic Programming, 2011 - Elsevier
The family of domain algebras provide an elegant formal system for automated reasoning
about programme verification. Their primary models are algebras of relations, viz …

[HTML][HTML] The algebra of functions with antidomain and range

R Hirsch, M Jackson, S Mikulás - Journal of Pure and Applied Algebra, 2016 - Elsevier
We give complete, finite quasiequational axiomatisations for algebras of unary partial
functions under the operations of composition, domain, antidomain, range and intersection …

Taming multirelations

H Furusawa, G Struth - ACM Transactions on Computational Logic …, 2016 - dl.acm.org
Binary multirelations generalise binary relations by associating elements of a set to its
subsets. We study the structure and algebra of multirelations under the operations of union …

Dependently-typed formalisation of relation-algebraic abstractions

W Kahl - Relational and Algebraic Methods in Computer …, 2011 - Springer
We present a formalisation in the dependently-typed programming language Agda2 of basic
category and allegory theory, and of generalised algebras where function symbols are …

lr-Multisemigroups and modal convolution algebras

U Fahrenberg, C Johnsen, G Struth… - arXiv preprint arXiv …, 2021 - arxiv.org
We show how modal quantales arise as convolution algebras of functions from lr-
multisemigroups that is, multisemigroups with a source map l and a target map r, into modal …