On neighborhood product of some Horn axiomatizable logics

TL;DR

This paper investigates the product of neighborhood frames in modal logic, providing new characterizations of n-products for certain Horn axiomatizable logics and applications to topological spaces.

Contribution

It introduces the n-product of modal logics based on neighborhood frames and determines these products for pretransitive Horn axiomatizable logics, including topological space applications.

Findings

n-product of two pretransitive Horn axiomatizable logics characterized

d-logic of product spaces identified for specific classes

extends understanding of modal logic products in neighborhood semantics

Abstract

We consider modal logics of products of neighborhood frames. We define n-product of modal logics as the logic of all products of neighborhood frames of corresponding logics and find n-product of any two pretransitive Horn axiomatizable logics. As a corrolary we find the d-logic of products of topological spaces for some classes of topological spaces.