Aug 2026· Studia Logica: An International Journal for Symbolic Logic· 1 citation· 16 references
Abstract
Bochvar algebras and regular double Stone algebras are the equivalent algebraic semantics of logics widely used for reasoning about partial information in computer science and AI. Viewed as categories, they are both equivalent to certain categories based on Boolean algebras. Despite this similarity, the precise relationship between Bochvar algebras and regular double Stone algebras has not been clearly established. In this paper, we obtain the following main results:
i)
we provide a different proof of the categorical equivalence result for Bochvar algebras, using a modified twist product construction in place of a Płonka sum construction;
ii)
we show that the functor witnessing this equivalence can be decomposed into a standard twist product and a translation map yielding Bochvar algebras as term reducts of regular double Stone algebras;
iii)
we prove that the algebraic category of regular double Stone algebras is equivalent to a full and reflective subcategory of the category of Bochvar algebras, and (with certain provisos) that the embedding functor is dense – namely, every Bochvar algebra arises as a colimit of its regular double Stone subalgebras.
Algebras of disjoint alternatives (ADAs), introduced by Manes, are extensions of McCarthy algebras by a unary operator acting as an oracle for the halting problem, and provide a semantics for the equational theory of the
if–then–else
construct.
We study the variety of ADAs in the signature without the constan...
G. Vergottini, A. Ledda, P. Graziani· Mathematical Logic Quarterly· 0 citations
Sequent algebras were introduced by D. Vakarelov \cite{VakarelovSequentALg} as a generalization of contact algebras, replacing the binary contact relation with a relation between finite sets of regions and regions. In this paper, we present sequent algebras as Boolean algebras endowed with a finitary closure operator s...
In this paper we develop several aspects of the algebraic theory of Girard algebras, regarded as the equivalent algebraic semantics of multiplicative additive Linear Logic $\mathsf{MALL}$. The main structural results concern the bottom of the subvariety lattice of the variety of Girard algebras: varieties generated by...
We describe a (combinatorial, monoidal, Cat-enriched) Quillen model structure on the category of Cartmell's generalized algebraic theories (gats); its homotopy bicategory consists essentially of Taylor's rooted display map categories. This allows us to compare two kinds of morphisms of gats: one where sort dependency a...
We prove Z-stability for all simple, separable, pure, nuclear C*-algebras. Combining this with very recent work of Thiel completes the proof of the Toms-Winter conjecture. We do this through the framework of II_1 factorial tracially complete C*-algebras. We characterise regularity for these algebras in various terms. I...
Samuel Evington, Shan-Shan Hua, Christopher P. Schafhauser et al.· 0 citations
Highest weight categories with finitely many simples correspond to quasi-hereditary algebras. Ringel duality shows that, up to Morita equivalence, quasi-hereditary algebras come in pairs, while Ringel self-duality is the phenomenon in which a quasi-hereditary algebra is paired with itself. The main purpose of this pape...
Tiago Cruz· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
