Neighbourhood semantics for graded modal logic

TL;DR

This paper introduces a new class of neighbourhood frames for graded modal logic, embedding Kripke frames into them, and explores their definability and bisimulation properties.

Contribution

It presents a novel class of neighbourhood frames for graded modal logic, embedding Kripke frames and defining a new graded bisimulation.

Findings

Neighbourhood frames are first-order definable.

They are not modally definable.

A new graded bisimulation is introduced.

Abstract

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation.