## Cut elimination for a class of propositional based logics (2005)

Citations: | 4 - 2 self |

### BibTeX

@TECHREPORT{Rasga05cutelimination,

author = {J. Rasga},

title = {Cut elimination for a class of propositional based logics},

institution = {},

year = {2005}

}

### OpenURL

### 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

567 |
Untersuchungen über das logische Schließen
- Gentzen
- 1935
(Show Context)
Citation Context ...tural logics. Mathematics Subject Classification 2000. 03F05, 03F07, 03F03. 1 Introduction Cut elimination has been studied for a wide variety of logics, but most of the times in a case by case basis =-=[7, 4, 2, 3]-=-. There is no general characterization of the properties a sequent calculus should satisfy in order to enjoy cut elimination, with the noble exception of display logic [3, 9, 16]. Herein conditions fo... |

186 | Fresh logic
- Gabbay
- 2007
(Show Context)
Citation Context ... rules and provisos is also an interesting direction of future work [11, 10]. Another interesting topic is the investigation of the preservation of the conditions obtained in this paper under fibring =-=[6, 5, 13]-=-. Finally it would certainly be interesting to broaden the properties investigated to, for instance, the Beth definability property and the Craig interpolation property. 146 Acknowledgments The autho... |

106 |
Display logic
- Belnap
- 1982
(Show Context)
Citation Context ...tural logics. Mathematics Subject Classification 2000. 03F05, 03F07, 03F03. 1 Introduction Cut elimination has been studied for a wide variety of logics, but most of the times in a case by case basis =-=[7, 4, 2, 3]-=-. There is no general characterization of the properties a sequent calculus should satisfy in order to enjoy cut elimination, with the noble exception of display logic [3, 9, 16]. Herein conditions fo... |

78 | editor. Handbook of Proof Theory
- Buss
- 1998
(Show Context)
Citation Context ...tural logics. Mathematics Subject Classification 2000. 03F05, 03F07, 03F03. 1 Introduction Cut elimination has been studied for a wide variety of logics, but most of the times in a case by case basis =-=[7, 4, 2, 3]-=-. There is no general characterization of the properties a sequent calculus should satisfy in order to enjoy cut elimination, with the noble exception of display logic [3, 9, 16]. Herein conditions fo... |

44 |
Normal derivability in classical logic
- Tait
- 1968
(Show Context)
Citation Context ...re provisos, and the axiom rule. QED 4 Cut elimination In this section we show that any calculus that is cut suitable enjoys cut elimination. The proof follows the Tait style proof of cut elimination =-=[14]-=- as described in [15]. We start by introducing some basic definitions needed in the cut elimination proof. Our reference is [15]. The depth of a formula ϕ, denoted by |ϕ|, is the maximum length of a b... |

38 | Substructural logics on display
- Goré
(Show Context)
Citation Context ... case by case basis [7, 4, 2, 3]. There is no general characterization of the properties a sequent calculus should satisfy in order to enjoy cut elimination, with the noble exception of display logic =-=[3, 9, 16]-=-. Herein conditions for logics in a certain class to enjoy cut elimination are investigated and a general proof of cut elimination is presented for the logics satisfying that conditions. These conditi... |

32 |
Non-deterministic Multiple-valued Structures
- Avron, Lev
- 2001
(Show Context)
Citation Context ...n rules, but not contemplating the condition relative to the relation between the number of premises in the cut sequence and the multiplicative and additive character of the rules, is also present in =-=[1]-=-. 3.1 Cut suitable calculus The conditions allowing that a calculus enjoy cut elimination, are put together in the definition of a cut suitable calculus. Definition 3.3 A sequent calculus is cut suita... |

20 | Modulated fibring and the collapsing problem
- Sernadas, Rasga, et al.
(Show Context)
Citation Context ... rules and provisos is also an interesting direction of future work [11, 10]. Another interesting topic is the investigation of the preservation of the conditions obtained in this paper under fibring =-=[6, 5, 13]-=-. Finally it would certainly be interesting to broaden the properties investigated to, for instance, the Beth definability property and the Craig interpolation property. 146 Acknowledgments The autho... |

16 |
Cut normal forms and proof complexity
- Baaz, Leitsch
- 1999
(Show Context)
Citation Context |

10 |
Indexed systems of sequents and cut-elimination
- Mints
- 1997
(Show Context)
Citation Context ...context is an interesting topic [12]. The extension to more general type of sequents, or to sequent calculi with a wider universe of rules and provisos is also an interesting direction of future work =-=[11, 10]-=-. Another interesting topic is the investigation of the preservation of the conditions obtained in this paper under fibring [6, 5, 13]. Finally it would certainly be interesting to broaden the propert... |

9 | Sufficient conditions for cut elimination with complexity analysis
- Rasga
(Show Context)
Citation Context ...finite time. Interesting directions of future work can be devised. The extension to first order based logics and the study of the complexity of cut elimination in this context is an interesting topic =-=[12]-=-. The extension to more general type of sequents, or to sequent calculi with a wider universe of rules and provisos is also an interesting direction of future work [11, 10]. Another interesting topic ... |

7 | Modal sequent calculi labelled with truth values: Completeness, duality and analyticity
- Mateus, Sernadas, et al.
(Show Context)
Citation Context ...context is an interesting topic [12]. The extension to more general type of sequents, or to sequent calculi with a wider universe of rules and provisos is also an interesting direction of future work =-=[11, 10]-=-. Another interesting topic is the investigation of the preservation of the conditions obtained in this paper under fibring [6, 5, 13]. Finally it would certainly be interesting to broaden the propert... |

7 |
Strong cut-elimination in display logic
- Wansing
- 1995
(Show Context)
Citation Context ... case by case basis [7, 4, 2, 3]. There is no general characterization of the properties a sequent calculus should satisfy in order to enjoy cut elimination, with the noble exception of display logic =-=[3, 9, 16]-=-. Herein conditions for logics in a certain class to enjoy cut elimination are investigated and a general proof of cut elimination is presented for the logics satisfying that conditions. These conditi... |

3 | Heterogeneous fibring of deductive systems via abstract proof systems
- Cruz-Filipe, Sernadas, et al.
- 2005
(Show Context)
Citation Context ... rules and provisos is also an interesting direction of future work [11, 10]. Another interesting topic is the investigation of the preservation of the conditions obtained in this paper under fibring =-=[6, 5, 13]-=-. Finally it would certainly be interesting to broaden the properties investigated to, for instance, the Beth definability property and the Craig interpolation property. 146 Acknowledgments The autho... |