Layers of zero probability and stable coherence over Łukasiewicz events

Tommaso Flaminio, Lluis Godo

The notion of stable coherence has been recently introduced to characterize coherent assignments to conditional many-valued events by means of hyperreal-valued states. In a nutshell, an assignment, or book, β on a finite set of conditional events is stably coherent if there exists a coherent variant β of β such that β maps all antecedents of conditional events to a strictly positive hyperreal number, and such that β and β differ by an infinitesimal. In this paper, we provide a characterization of stable coherence in terms of layers of zero probability for books on Łukasiewicz logic events.

Keywords: Layers of zero probability, Conditional probability, Stable coherence MV-algebras. 

Volume 21, Issue 1, pp. 113–123.

Equivalences between subcategories of MTL-algebras via Boolean algebras and prelinear semihoops

Stefano Aguzzoli, Tommaso Flaminio, Sara Ugolini

This article studies the class of strongly perfect MTL-algebras, i.e. MTL-algebras having an involutive co-radical, and the variety they generate, namely SBP0. Once these structures will be introduced, we will first establish categorical equivalences for several of their relevant proper subvarieties by employing a generalized notion of triplets whose main components are a Boolean algebra and a prelinear semihoop. When triplets are further expanded by a suitable operation between their semihoop reducts, we define a category of quadruples that are equivalent to the whole category of SBP0-algebras. Finally, we will provide an explicit representation of SBP0-algebras in terms of (weak) Boolean products.

Keywords: Strongly perfect MTL-algebras, Boolean Algebras, Prelinear Semihoops, Categorical Equivalence

Journal of Logic and Computation, exx014, https://doi.org/10.1093/logcom/exx014