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Preservation of interpolation features by fibring
 Journal of Logic and Computation
"... Fibring is a metalogical constructor that permits to combine different logics by operating on their deductive systems under certain natural restrictions, as for example that the two given logics are presented by deductive systems of the same type. Under such circumstances, fibring will produce a new ..."
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Cited by 9 (9 self)
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Fibring is a metalogical constructor that permits to combine different logics by operating on their deductive systems under certain natural restrictions, as for example that the two given logics are presented by deductive systems of the same type. Under such circumstances, fibring will produce a new deductive system by means of the free use of inference rules from both deductive systems, provided the rules are schematic, in the sense of using variables that are open for application to formulas with new linguistic symbols (from the point of view of each logic component). Fibring is a generalization of fusion, a less general but wider developed mechanism which permits results of the following kind: if each logic component is decidable (or sound, or complete with respect to a certain semantics) then the resulting logic heirs such a property. The interest for such preservation results for combining logics is evident, and they have been achieved in the more general setting of fibring in several cases. The Craig interpolation property and the Maehara interpolation have a special significance when combining logics, being related to certain problems of complexity theory, some properties of model theory and to the usual (global) metatheorem of deduction. When the peculiarities of the distinction between local and global deduction interfere, justifying what we call careful reasoning, the question of preservation of interpolation becomes more subtle and other forms of interpolation can be distinguished. These questions are investigated and several (global and local) preservation results for interpolation are obtained for fibring logics that fulfill mild requirements. AMS Classification: 03C40, 03B22, 03B45 1
Plain fibring and direct union of logics with matrix semantics
 Proceedings of the 2nd Indian International Conference on Artificial Intelligence (IICAI 2005
, 2005
"... Abstract. In this paper a variation of the fibred semantics of D. Gabbay called plain fibring is proposed, with the aim of combining logics given by matrix semantics. It is proved that the plain fibring of matrix logics is also a matrix logic. Moreover, it is proved that any logic obtained by plain ..."
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Cited by 4 (4 self)
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Abstract. In this paper a variation of the fibred semantics of D. Gabbay called plain fibring is proposed, with the aim of combining logics given by matrix semantics. It is proved that the plain fibring of matrix logics is also a matrix logic. Moreover, it is proved that any logic obtained by plain fibring is a conservative extension of the original logics. It is also proposed a simpler version of plain fibring of matrix logics called direct union. This technique is applied to the study of the class of fuzzy logics defined by tnorms.
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.
Parallel composition of logics — Semantics
 Preprint, SQIG  IT and IST  TU Lisbon
, 2010
"... Capitalizing on the graphtheoretic account of logic systems and their fibrings in [25], and inspired on notions of concurrency, a novel form of combination of logics — parallel composition — is proposed at the semantic level. Parallel composition allows both symmetric (like sharing) and nonsymmetr ..."
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Cited by 2 (2 self)
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Capitalizing on the graphtheoretic account of logic systems and their fibrings in [25], and inspired on notions of concurrency, a novel form of combination of logics — parallel composition — is proposed at the semantic level. Parallel composition allows both symmetric (like sharing) and nonsymmetric (like triggering) forms of interaction to be specified at the signature level. Parallel composition subsumes fibring as a special case. Parallel composition is presented using universal constructions in the categories of signatures and interpretations, using a cofibration for synchronization. The conservative nature of parallel composition under lossless synchronization is established using a generalized bisimulation technique. The conservative nature of free parallel composition and unconstrained fibring follow as corollaries.
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
Cryptofibring ∗
"... Fibring is recognized as one of the main mechanisms for combining logics [3, 5, 6], namely because many general results for preservation of soundness and completeness have been established, eg. [8, 1]. However, fibring suffers from an anomaly usually known as “the collapsing problem ” [2, 4]. Indeed ..."
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Fibring is recognized as one of the main mechanisms for combining logics [3, 5, 6], namely because many general results for preservation of soundness and completeness have been established, eg. [8, 1]. However, fibring suffers from an anomaly usually known as “the collapsing problem ” [2, 4]. Indeed, ever since