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Reihane Zoghifard

Publications and source records attributed to Reihane Zoghifard.

6 recordsLinked to original sources
arXiv2026

Goldblatt-Thomason Theorem for Probability Logic

Probability logic (PL) extends propositional logic with countably many probability operators, one for each rational number between 0 and 1. The formulas of this logic are interpreted over the class of Markov processes, i.e., structures of the form $(Ω, Σ, T)$, where$(Ω, Σ)$ is a measurable space and $T$ is a Markov kernel. The main contribution of this paper is the establishment of the Goldblatt-Thomason theorem for probability logic. As an application, we show that the class of Harsanyi type spaces is definable in PL. Moreover, we obtain some variants of the Goldblatt-Thomason theorem for specific subclasses of Markov processes.

cs.LO↗
arXiv2026

Strong Completeness of Provability Logic for Uncountable Languages

For an ordinal $λ>0$, we use the Erdős--Rado partition theorem to prove the failure of strong completeness of $\mathsf{GL}$ for modal languages of cardinality $(2^{|λ|+\aleph_0})^{+}$ with respect to models on ordinals equipped with the generalized Icard topologies $\mathcal{I}_λ$ and ${τ_{c}}_{+λ}$. Specifically, we show that for such languages there exists a $\mathsf{GL}$-consistent set of formulas having neither $(Θ, \mathcal{I}_λ)$-model nor $(Θ, {τ_{c}}_{+λ})$-model. We also introduce two kinds of natural classes of topological spaces, called \emph{ $λ$-bouquet spaces} and \emph{ultralinear $λ$-bouquet spaces}, and prove that they yield strong completeness of $\mathsf{GL}$ and $\mathsf{GL}.3$ respectively for languages of cardinality $λ$.

math.LO↗
arXiv2021

A Lindström theorem for intuitionistic first-order logic

We extend the main result of (G. Badia and G. Olkhovikov. A Lindström theorem for intuitionistic propositional logic. Notre Dame Journal of Formal Logic, 61 (1): 11--30 (2020)) to the first-order intuitionistic logic (with and without equality), showing that it is the maximal (with respect to expressive power) abstract logic satisfying a certain form of compactness, the Tarski union property and preservation under asimulations. A similar result is also shown for the intuitionistic logic of constant domains.

math.LO↗
arXiv2018

Probability Logic: A Model Theoretic Perspective

In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $σ$-additive probability models, and subsequently when this class of models is considered it is shown that the compactness property holds with respect to a fragment of $PL$ called basic probability logic ($BPL$). On the other hand, when dealing with finitely-additive probability models, one may extend the compactness property for a larger fragment of probability logic, namely positive probability logic ($PPL$). We finally prove that while the Löwenheim-Skolem number of the class of $σ$-additive probability models is uncountable, it is $\aleph_0$ for the class of finitely additive probability models.

math.LO↗