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16
Fibring Logics with Topos Semantics
, 2002
"... The concept of fibring is extended to higherorder logics with arbitrary modalities and binding operators. A general completeness theorem is established for such logics including HOL and with the metatheorem of deduction. As a corollary, completeness is shown to be preserved when fibring such rich ..."
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Cited by 11 (6 self)
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The concept of fibring is extended to higherorder logics with arbitrary modalities and binding operators. A general completeness theorem is established for such logics including HOL and with the metatheorem of deduction. As a corollary, completeness is shown to be preserved when fibring such rich logics. This result is extended to weaker logics in the cases where fibring preserves conservativeness of HOLenrichments. Soundness is shown to be preserved by fibring without any further assumptions.
Modal Sequent Calculi Labelled with Truth Values: Completeness, Duality and Analyticity
 LOGIC JOURNAL OF THE IGPL
, 2003
"... Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessi ..."
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Cited by 7 (5 self)
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Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural twosorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result
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 ..."
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Cited by 4 (2 self)
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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.
Completeness Results for Fibred Parchments Beyond the Propositional Base
 Recent Trends in Algebraic Development Techniques  Selected Papers, volume 2755 of Lecture Notes in Computer Science
, 2003
"... In [6] it was shown that fibring could be used to combine institutions presented as cparchments, and several completeness preservation results were established. However, their scope of applicability was limited to propositionalbased logics. Herein, we extend these results to a broader class of ..."
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Cited by 4 (3 self)
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In [6] it was shown that fibring could be used to combine institutions presented as cparchments, and several completeness preservation results were established. However, their scope of applicability was limited to propositionalbased logics. Herein, we extend these results to a broader class of logics, possibly including variables, terms and quantifiers.
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 ..."
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Cited by 4 (3 self)
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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
Heterogeneous fibring of deductive systems via abstract proof systems
, 2005
"... Fibring is a metalogical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way (e.g via Hilbert calculi). Heterogeneous fibring, allowing the original logics to have ..."
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Cited by 3 (1 self)
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Fibring is a metalogical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way (e.g via Hilbert calculi). Heterogeneous fibring, allowing the original logics to have different presentations (e.g. one presented by a Hilbert calculus and the other by a sequent calculus), has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semidecidability is investigated.
Graphtheoretic fibring of logics
 Part II  Completeness preservation. Preprint, SQIG  IT and IST  TU Lisbon
, 2008
"... A graphtheoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as an mgraph where the nodes and the medges include the sorts and the constructors of the signatu ..."
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Cited by 3 (3 self)
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A graphtheoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as an mgraph where the nodes and the medges include the sorts and the constructors of the signatures at hand. Fibring of two models is an mgraph where the nodes and the medges are the values and the operations in the models, respectively. Fibring of two deductive systems is an mgraph whose nodes are language expressions and the medges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graphtheoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with nondeterministic semantics, logics with an algebraic semantics, logics with partial semantics, and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. 1
TruthValues as Labels: A General Recipe for Labelled Deduction
"... We introduce a general recipe for presenting nonclassical logics in a modular and uniform way as labelled natural deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truthvalues. ..."
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Cited by 1 (1 self)
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We introduce a general recipe for presenting nonclassical logics in a modular and uniform way as labelled natural deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truthvalues.
Preservation of interpolation by fibring
 In Carnielli et al. [2004a
"... The method of fibring for combining logics as originally proposed by Gabbay [13, 14], includes some other methods as fusion [29] as a special case. Albeit fusion is the best developed mechanism, mainly in what concerns preservation of properties as ..."
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Cited by 1 (1 self)
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The method of fibring for combining logics as originally proposed by Gabbay [13, 14], includes some other methods as fusion [29] as a special case. Albeit fusion is the best developed mechanism, mainly in what concerns preservation of properties as
Bridge principles and combined reasoning
"... Hume’s wellknown objection on the purported connections between ‘is’ and ‘ought ’ in philosophical argumentation gave rise to a quarrel about the legitimacy of statements that bind factualities to norms. The idea of bridge principle has been inaugurated as statements which precisely crystallize pri ..."
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Hume’s wellknown objection on the purported connections between ‘is’ and ‘ought ’ in philosophical argumentation gave rise to a quarrel about the legitimacy of statements that bind factualities to norms. The idea of bridge principle has been inaugurated as statements which precisely crystallize principles of mixed reasoning. We critically examine the role of bridge principles within the context of combination of logics, emphasizing situations where such principles spontaneously arise with desirable and undesirable consequences for combined reasoning. 1 Bridge principles and combined logics As wittily put in [17], nobody knows how many times the passage from David Hume’s “A Treatise of Human Nature ” (cf. [16], Book 3, Part 1, Section 1, paragraph 27) has been quoted. This passage that generated a neverending controversy and so many quotations attests that many times people (philosophers, perhaps) draw conclusions involving imperative