Free logics: variants, unification, and some applications

• Applicant: Dr. Norbert Gratzl
• Subject Area: Theoretical Philosophy
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 459928802

The continuation of the project "Free logic - variants, unification and some applications" aims to expand and delve deeper into the results of the original project. That is to say, there are three areas to be investigated: (1) modal free logic, (2) frame properties and geometrization, and (3) the third value in free logics. Based on the findings that quantifiers and modal operators are treatable "on par" we aim to bring together the different approaches to free and modal logic investigated in the literature under one formal umbrella. So areas (1) and (2) are connected naturally both proof- and model-theoretically. Where the unifying force really stems from is the possibility of accepting a third semantical value (area (3)), which allows for a joint presentation of various systems, based on several different understandings of the third value. More theoretical work indicated above - unified in the intersection of all three areas under investigation - will then find its philosophical application in modal epistemology.

• DFG Programme: Research Grants