Results 1 
3 of
3
Cut elimination for a class of propositional based logics
, 2005
"... 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 fragme ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
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.
Recovering a logic from its fragments by metafibring. Logica Universalis
 In print. Preliminary version available at CLE ePrints 5(4), 2005. URL = http://www.cle.unicamp.br/eprints/vol 5,n 4,2005.html
"... In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some metaproperties of the connectives are lost after ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some metaproperties of the connectives are lost after the combination process. In order to overcome this problem, the categories Mcon and Seq of multipleconclusion consequence relations and sequent calculi, respectively, are introduced. The main feature of these categories is the preservation, by morphisms, of metaproperties of the consequence relations, which allows, in several cases, to recover a logic by fibring of its fragments. The fibring in this categories is called metafibring. Several examples of wellknown logics which can be recovered by metafibring its fragments (in opposition to fibring in the usual categories) are given. Finally, a general semantics for objects in Seq (and, in particular, for objects in Mcon) is proposed, obtaining a category of logic systems
The essence of proofs when fibring sequent calculi
"... Combining logics in an important topic in applied logics [7, 1] that raises interesting theoretical problems related to transference results. The objective is to produce a new logic from two (or more) given logics by using a meta operator – the combination mechanism. Of special interest is to invest ..."
Abstract
 Add to MetaCart
Combining logics in an important topic in applied logics [7, 1] that raises interesting theoretical problems related to transference results. The objective is to produce a new logic from two (or more) given logics by using a meta operator – the combination mechanism. Of special interest is to investigate whether the mechanism preserves logical properties of the original logics. In general, sufficient conditions can be given for preservation. Fibring, proposed by Gabbay in [5], is one of the most challenging mechanisms for combining logics, which includes fusion of modal logics [10] as a particular case. Fibring can be and has been investigated from a deductive point of view (mainly using Hilbert calculi [11], labelled deductive systems [8] and tableau systems [2]) and also from a modeltheoretic perspective (using either an algebraic approach or a modallike semantics [6]). Several transference results have been obtained for these constructions, namely for soundness and completeness [11], several guises of interpolation and semidecidability. Up to now, work on fibring sequent calculi has not been considered. A possibility