From Coalgebraic Logic to Modal Logic: An Introduction

We present how modalities in coalgebraic logic can be introduced to describe behavior of the systems. We start with an analysis of coalgebraic approach together with several simply understandable examples of coalgebras. We concern on observable behaviour of the systems that can be described by coalgebraic formulas. We extend this logic with modalities of necessity and possibility to increase the expressive power of coalgebraic logic. We illustrate our approach on the same examples to compare both approaches.