LFCS Seminar: Tuesday 5th May: Greg Restall Greg RestallTue, 05 May, 4.10pm Venue: IF G.03 Title: Thoroughly Linear Hypersequents Abstract In this talk I will introduce a simple hypersequent calculus for the propositional modal logic S5, explaining how this representation encodes a natural form of reasoning about possibility and necessity. I then explain how the familiar structural rules of contraction and weakening take two forms in such a hypersequent calculus: they operate inside sequents, as familiar in substructural logics (linear logic, relevant logics, affine logic, etc.), but they also take an outer form, governing weakening or contraction of zones in a sequent. This motivates the formulation of a thoroughly linear hypersequent modal logic, in which we do without both inner and outer forms of contraction and weakening. This results in a novel modal logic, with a cut-free hypersequent calculus giving a straightforward decision procedure. Simple models (algebras) can be used to show how the logic differs from classical S5. These results help us understand the relationship between operational rules and structural rules in a generalised sequent calculus setting. The talk ends with some gestures toward open problems and possible applications. Bio: Greg Restall is Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology. He received his Ph.D. from the University of Queensland in 1994, and has held positions at the Australian National University, Macquarie University, and the University of Melbourne. His research focuses on logic, and its connections to issues in language, epistemology and metaphysics. He is the author of An Introduction to Substructural Logics (Routledge, 2000), Logic (Routledge, 2006), Logical Pluralism(Oxford University Press, 2006; with Jc Beall) and Logical Methods (MIT Press, 2023; with Shawn Standefer). He is a Fellow of the Australian Academy of the Humanities. His personal website is https://consequently.org. May 05 2026 16.10 - 17.00 LFCS Seminar: Tuesday 5th May: Greg Restall Greg Restall University of St Andrews https://consequently.org Informatics Forum, G.03
LFCS Seminar: Tuesday 5th May: Greg Restall Greg RestallTue, 05 May, 4.10pm Venue: IF G.03 Title: Thoroughly Linear Hypersequents Abstract In this talk I will introduce a simple hypersequent calculus for the propositional modal logic S5, explaining how this representation encodes a natural form of reasoning about possibility and necessity. I then explain how the familiar structural rules of contraction and weakening take two forms in such a hypersequent calculus: they operate inside sequents, as familiar in substructural logics (linear logic, relevant logics, affine logic, etc.), but they also take an outer form, governing weakening or contraction of zones in a sequent. This motivates the formulation of a thoroughly linear hypersequent modal logic, in which we do without both inner and outer forms of contraction and weakening. This results in a novel modal logic, with a cut-free hypersequent calculus giving a straightforward decision procedure. Simple models (algebras) can be used to show how the logic differs from classical S5. These results help us understand the relationship between operational rules and structural rules in a generalised sequent calculus setting. The talk ends with some gestures toward open problems and possible applications. Bio: Greg Restall is Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology. He received his Ph.D. from the University of Queensland in 1994, and has held positions at the Australian National University, Macquarie University, and the University of Melbourne. His research focuses on logic, and its connections to issues in language, epistemology and metaphysics. He is the author of An Introduction to Substructural Logics (Routledge, 2000), Logic (Routledge, 2006), Logical Pluralism(Oxford University Press, 2006; with Jc Beall) and Logical Methods (MIT Press, 2023; with Shawn Standefer). He is a Fellow of the Australian Academy of the Humanities. His personal website is https://consequently.org. May 05 2026 16.10 - 17.00 LFCS Seminar: Tuesday 5th May: Greg Restall Greg Restall University of St Andrews https://consequently.org Informatics Forum, G.03
May 05 2026 16.10 - 17.00 LFCS Seminar: Tuesday 5th May: Greg Restall Greg Restall University of St Andrews https://consequently.org
