arXiv subjects

Majid Alizadeh

Publications and source records attributed to Majid Alizadeh.

7 recordsLinked to original sources

arXiv2025

A Cut-free Sequent Calculus for Basic Intuitionistic Dynamic Topological Logic

As part of a broader family of logics, [1, 3] introduced two key logical systems: $\mathsf{iK_{d}}$, which encapsulates the basic logical structure of dynamic topological systems, and $\mathsf{iK_{d*}}$, which provides a well-behaved yet sufficiently general framework for an abstract notion of implication. These logics have been thoroughly examined through their algebraic, Kripke-style, and topological semantics. To complement these investigations with their missing proof-theoretic analysis, this paper introduces a cut-free G3-style sequent calculus for $\mathsf{iK_{d}}$ and $\mathsf{iK_{d*}}$. Using these systems, we demonstrate that they satisfy the disjunction property and, more broadly, admit a generalization of Visser's rules. Additionally, we establish that $\mathsf{iK_{d}}$ enjoys the Craig interpolation property and that its sequent system possesses the deductive interpolation property.

math.LO↗

arXiv2024

On a Generalization of Heyting Algebras II

A $\nabla$-algebra is a natural generalization of a Heyting algebra, unifying several algebraic structures, including bounded lattices, Heyting algebras, temporal Heyting algebras, and the algebraic representation of dynamic topological systems. In the prequel to this paper [3], we explored the algebraic properties of various varieties of $\nabla$-algebras, their subdirectly-irreducible and simple elements, their closure under Dedekind-MacNeille completion, and their Kripke-style representation. In this sequel, we first introduce $\nabla$-spaces as a common generalization of Priestley and Esakia spaces, through which we develop a duality theory for certain categories of $\nabla$-algebras. Then, we reframe these dualities in terms of spectral spaces and provide an algebraic characterization of natural families of dynamic topological systems over Priestley, Esakia, and spectral spaces. Additionally, we present a ring-theoretic representation for some families of $\nabla$-algebras. Finally, we introduce several logical systems to capture different varieties of $\nabla$-algebras, offering their algebraic, Kripke, topological, and ring-theoretic semantics, and establish a deductive interpolation theorem for some of these systems.

math.LO↗

arXiv2024

On a Generalization of Heyting Algebras I

$\nabla$-algebra is a natural generalization of Heyting algebra, unifying many algebraic structures including bounded lattices, Heyting algebras, temporal Heyting algebras and the algebraic presentation of the dynamic topological systems. In a series of two papers, we will systematically study the algebro-topological properties of different varieties of $\nabla$-algebras. In the present paper, we start with investigating the structure of these varieties by characterizing their subdirectly irreducible and simple elements. Then, we prove the closure of these varieties under the Dedekind-MacNeille completion and provide the canonical construction and the Kripke representation for $\nabla$-algebras by which we establish the amalgamation property for some varieties of $\nabla$-algebras. In the sequel of the present paper, we will complete the study by covering the logics of these varieties and their corresponding Priestley-Esakia and spectral duality theories.

math.LO↗

arXiv2022

Meet MASKS: A novel Multi-Classifier's verification approach

In this study, a new ensemble approach for classifiers is introduced. A verification method for better error elimination is developed through the integration of multiple classifiers. A multi-agent system comprised of multiple classifiers is designed to verify the satisfaction of the safety property. In order to examine the reasoning concerning the aggregation of the distributed knowledge, a logical model has been proposed. To verify predefined properties, a Multi-Agent Systems' Knowledge-Sharing algorithm (MASKS) has been formulated and developed. As a rigorous evaluation, we applied this model to the Fashion-MNIST, MNIST, and Fruit-360 datasets, where it reduced the error rate to approximately one-tenth of the individual classifiers.

cs.AI↗

arXiv2022

Linear Temporal Public Announcement Logic: a new perspective for reasoning about the knowledge of multi-classifiers

In this note, a formal transition system model called LTPAL to extract knowledge in a classification process is suggested. The model combines the Public Announcement Logic (PAL) and the Linear Temporal Logic (LTL). In the model, first, we consider classifiers, which capture single-framed data. Next, we took classifiers for data-stream data input into consideration. Finally, we formalize natural language properties in LTPAL with a video-stream object detection sample.

cs.AI↗

arXiv2020

Understanding Epidemic Data and Statistics: A case study of COVID-19

The 2019-Novel-Coronavirus (COVID-19) has affected 116 countries (By March 12) and out of more than 118,000 confirmed cases. Understanding the transmission dynamics of the infection in each country which affected on a daily basis and evaluating the effectiveness of control policies is critical for our further actions. To date, the statistics of COVID-19 reported cases show more than 80 percent of infected had a mild case of disease, while around 14 percent of infected experienced a severe one and about 5 percent are categorized as critical disease victims. Today's report (2020-03-12; daily updates in the prepared website) shows the confirmed cases of COVID-19 in China, South Korea, Italy, and Iran are 80932, 7869, 12462 and 10075; respectively. Calculating the total Case Fatality Rate (CFR) of Italy (2020-03-04), about 7.9% of confirmed cases passed away. Compared to South Korea's rate of 0.76% (10 times lower than Italy) and China's 3.8% (50% lower than Italy), the CFR of Italy is too high. There are some effective policies that yield significant changes in the trend of cases. The lockdown policy in China and Italy (the effect observed after 11 days), Shutdown of all nonessential companies in Hubei (the effect observed after 5 days), combined policy in South Korea and reducing working hours in Iran.

q-bio.PE↗

arXiv2010

$M$-Shellability of Discrete Polymatroids

In this note we show that every discrete polymatroid is $M$-shellable. This gives, in a partial case, a positive answer to a conjecture of Chari and improves a recent result of Schweig where he proved that the $h$-vector of a lattice path matroid satisfies a conjecture of Stanley.

math.CO↗