Sara Negri – A three-fold method for non-classical logics

UConn Logic Group – Annual Logic Lecture, May 1, 2019

Sara Negri (Helsinki) – A three-fold method for non-classical logics

There are three established ways of analysing the validity of a logical argument: axiomatic, semantic, and inferential; they correspond to what could be called the normative, the descriptive, and the deductive face of a logical system and are tightly related to each other by fundamental meta-theorems.

For non-classical logics, each of the three aspects has drawbacks when considered in isolation. The situation changes, however, drastically when the three aspects are developed in parallel. Through the labelled formalism, by now is a well-developed methodology, models can be considered as purely mathematical objects with no ontological assumptions upon them: the semantics is turned into an essential component in the syntax of sequent calculi with invertible rules. Such calculi not only provide a tool for the automatisation of reasoning, but can also be used to establish very general properties of logical systems.