This project intends to study multiple conceptual applications of methods for combining logics. It shows how to combine alethic modal logics (in order to model the contingency operator) and epistemic logics. This combination is done with the aims of stating a kind of skepticism characterized by the following principle: contingent propositions are not known. This work also investigates connections between the notions of knowledge and belief. There is a famous argument called here knowledge-belief reduction which shows that both notions collapse. This project proposes the research, from the viewpoint of combining logics, of what are the combined formal systems able to avoid this collapse. By the end, modal combinations in contradictory environments are developed using the unifying tool called paraconsistentization of logics. This tool is used in order to paraconsistentize some combined logics in such way that one could get versions of logical skepticism where contradictions are not problematic, as well paraconsistent versions without the collapse of knowledge and belief. Another aim of the research is to investigate mathematical aspects of paraconsistentization of logics, as well its basic theory and applications.
News published in Agência FAPESP Newsletter about the scholarship: