The Hypersequent Approach to Modal Logic

Andrew Parisi

13 Feb, 2-3:30pm, LH 306

Various forms of inferentialism require a proof-theoretic account of modality. Many modal logics can be adequately captured with the sequent calculus. But there is no account yet discovered that can capture the full range of modal logics that might be of interest to inferentialists. In particular, no straightforward cut-free account of S5 has been discovered, and no account of logics much weaker than S4 can uniquely characterize the necessitation operator, i.e. a second necessitation operator with the same introduction rules is not everywhere intersubstitutible with the first necessitation operator. An alternative to sequents, hypersequents, is offered as a solution to some of these problems. Hypersequent accounts of various modal logics have been discovered that meet the above two criteria for an inferentialist account of the modal connectives. The various systems are obtained only by restrictions of the external structural rules of the hypersequent calculus.