As I venture deeper into my studies, I’m beginning to reaffirm my confidence in modal logic. This is primarily a function of seeing how it can be used at an applied/industrial level. I’m only beginning to understand, or in some cases, conjure, ways in which a logical model of a database, for instance, might be describable in modal propositional logic. Since I haven’t been able to achieve this at a sufficient level, I’ll hold off on sharing my exact thoughts. Needless to say, even this Stanford Encyclopedia of Philosophy entry on modal logic characterizes some of its commercial and/or industrial application.
The applications of modal logic to mathematics and computer science have become increasingly important. Provability logic is only one example of this trend. The term “advanced modal logic” refers to a tradition in modal logic research that is particularly well represented in departments of mathematics and computer science. This tradition has been woven into the history of modal logic right from its beginnings (Goldblatt, 2006). Research into relationships with topology and algebras represents some of the very first technical work on modal logic. However the term ‘advanced modal logic’ generally refers to a second wave of work done since the mid 1970s. Some example of the many interesting topics dealt with include results on decidability (whether it is possible to compute whether a formula of a given modal logic is a theorem) and complexity (the costs in time and memory needed to compute such facts about modal logics).
My recent attempt involved attempting to translate simple E-R logical data flows into modal propositions, though without quantification it was difficult and/or probably impossible.