Author name cluster
Melvin Fitting
Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.
Possible papers
4FLAP Journal 2015 Journal Article
Cut-Free Proof Systems for Geach Logics.
- Melvin Fitting
Prefixed tableaus for modal logics have been around since the early 1970s, and are quite familiar by now. Rather recently it was found that they were dual to nested sequents, which have a complicated history but which also trace back to the 1970’s. Both have provided very natural proof systems for the most common modal logics, including those in the so-called modal cube. In this paper we add some simple machinery to both prefixed tableaus and to nested sequents, producing cut-free proof systems for all logics axiomatized by Geach formulas, that is, by axiom schemes of the form ♦k l X ⊃ m ♦n X. This again provides proof mechanisms for the modal cube, but mechanisms of a different nature than usual. But further, it provides proof mechanisms for an infinite family of modal logics, and does so in a modular way with a clear separation between logical and structural rules. The version of nested sequents presented here has a direct relationship with the formal machinery of [23], and can be thought of as a notational variant of a natural and interesting fragment of what can be handled using that methodology.