Modal Logics of Relations

In other chapters we have seen or will see how logics from various origins can be treated in the unifying framework of multi-dimensional modal logic. In this chapter we will apply the same methodology to a very familiar logical system, namely that of first-order logic itself. Our modal analysis of the semantics of first-order logic naturally leads to the multi-dimensional perspective, and within this approach we will encounter some unexpected mysteries such as decidable versions of the predicate calculus.