Abstract

Sufficient conditions for propositional based logics to enjoy cut elimination are established. These conditions are satisfied by a wide class of logics encompassing among others classical and intuitionistic logic, modal logic S4, and classical and intuitionistic linear logic and some of their fragments. The class of logics is characterized by the type of rules and provisos used in their sequent calculi. The conditions can be checked in finite time and define relations between the rules and the provisos so that the calculus can enjoy cut elimination. A general proof of cut elimination is presented for any calculus satisfying those conditions.

Citations

493	Untersuchungen über das logische Schließen - Gentzen - 1935
162	Fibring logics - Gabbay - 1999
98	Display logic - Belnap - 1982
66	editor. The Handbook of Proof Theory - Buss - 1998
43	Normal derivability in classical logic - Tait - 1968
36	Substructural logics on display - Goré - 1998
22	Non-deterministic Multiple-valued Structures - Avron, Lev
17	Modulated fibring and the collapsing problem - Sernadas, Rasga, et al.
15	Cut Normal Forms and Proof Complexity - Baaz, Leitsch - 1999
9	Indexed systems of sequents and cut-elimination - Mints - 1997
9	Sufficient conditions for cut elimination with complexity analysis - Rasga
5	Modal sequent calculi labelled with truth values: Cut elimination - Mateus, Rasga, et al.
5	Strong cut-elimination in display logic - Wansing - 1995
3	Heterogeneous fibring of deductive systems via abstract proof systems - Cruz-Filipe, Sernadas, et al. - 2005