First-Order Modal $\xi$-Calculus: On the Aspects of Application and Bisimulation

TL;DR

This paper introduces first-order modal $\xi$-calculus and genealogical Kripke models, extending modal $$-calculus to better describe process genealogy and analyzing bisimulation within this framework.

Contribution

It presents a novel first-order modal $\xi$-calculus and genealogical Kripke models, expanding the expressivity of modal logic for process genealogy and bisimulation analysis.

Findings

Demonstrates the utility of the logic with vivid examples

Thoroughly examines bisimulation for the logic

Extends modal $$-calculus with new expressivity

Abstract

This paper proposes first-order modal $\xi$-calculus as well as genealogical Kripke models. Inspired by modal $\mu$-calculus, first-order modal $\xi$-calculus takes a quite similar form and extends its inductive expressivity onto a different dimension. We elaborate on several vivid examples that demonstrate this logic's profound utility, especially for depicting genealogy of concurrent computer processes. Bisimulation notion for the logic has also been thoroughly examined.