Tsinghua Tutorial: What makes logic (un)decidable?

What makes first-order logic undecidable and what makes modal logic decidable? This question can of course be answered in different ways. In this course, we explore one line of research that aims to answer this (and that has also provided a basis for many effective algorithms for reasoning problems in different areas of computer science), namely the study of guarded fragments of first-order logic (and of second-order logic). The guarded fragment of first-order logic was first introduced 25 years ago by Andreka, van Benthem and Nemeti, and is still very much alive today: the study of various aspects of (extensions of) the guarded fragment is still an active area of research up to this day.