Semantics and Ontology in Quantified Modal Logic

Philosophical logic studies the relationships between philosophical stands and logic as well as the logical and philosophical consequences that can be drawn from these connections. There is a good deal of results in this area spread over the second half of last century and, these days, there seems to be a renewed interest in this topic perhaps due to the introduction of ontological concerns in close areas like applied logic and knowledge representation. In this situation, it is important to provide an organized presentation where major philosophical systems and corresponding logics can be related and compared. Unfortunately, there is no systematic work in this direction (perhaps [1] is an exception). This work aims at a general formal framework where it is possible to study and compare some systems of quantified modal logic from the ontological perspective they embrace. The intention is to use the framework to consistently formalize important philosophical stands, namely, the endurantist, the perdurantist, and the sequentialist positions. Secondly, we want to use such a framework to formally evaluate the different ontological imports of these systems and to relate these results to specific philosophical arguments. Of course, a philosophical stand usually matches several formal systems (alternative options are available within the same philosophical perspective). Therefore, our approach consists in individuating a single formal system as paradigmatic for a philosophical view and to discuss its possible variants for relevant alternatives within that view. Here is the structure of this work.