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3 results

Implicational Kleene algebra with domain and the substructural logic of partial correctness
Igor Sedlár
Journal:

Mathematical Structures in Computer Science / Volume 34 / Issue 7 / August 2024

Published online by Cambridge University Press:

04 March 2024, pp. 645-660
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We show that Kozen and Tiuryn’s substructural logic of partial correctness $\mathsf{S}$ embeds into the equational theory of Kleene algebra with domain, $\mathsf{KAD}$. We provide an implicational formulation of $\mathsf{KAD}$ which sets $\mathsf{S}$ in the context of implicational extensions of Kleene algebra.

REPRESENTING REGULAR PSEUDOCOMPLEMENTED KLEENE ALGEBRAS BY TOLERANCE-BASED ROUGH SETS
Part of
JOUNI JÄRVINEN, SÁNDOR RADELECZKI
Journal:

Journal of the Australian Mathematical Society / Volume 105 / Issue 1 / August 2018

Published online by Cambridge University Press:

04 December 2017, pp. 57-78

Print publication:

August 2018
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We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.

Transferring Optimal Dualities: Theory and Practice
Part of
B. A. Davey, M. Haviar
Journal:

Journal of the Australian Mathematical Society / Volume 74 / Issue 3 / June 2003

Published online by Cambridge University Press:

09 April 2009, pp. 393-420

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June 2003
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Consider the quasi-variety generated by a finite algebra and assume that yields a natural duality on based on which is optimal modulo endomorphisms. We shoe that, provided satisfies certain minimality conditions, we can transfer this duality to a natural duality on based on , which is also optimal modulo endormorphisms, for any finite algebra in that has a subalgebra isomorphic to .