Logica Universalis 1 (2):377-416 (2007)
. 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 meta-properties of the connectives are lost after the combination process. In order to overcome this problem, the categories Mcon and Seq of multiple-conclusion consequence relations and sequent calculi, respectively, are introduced. The main feature of these categories is the preservation, by morphisms, of meta-properties 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 meta−fibring. Several examples of well-known logics which can be recovered by meta-fibring 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 called Log. A general theorem of preservation of completeness by fibring in Log is also obtained.
|Keywords||Fibring combinations of logics sequent calculi|
|Categories||categorize this paper)|
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Citations of this work BETA
Juxtaposition: A New Way to Combine Logics.Joshua Schechter - 2011 - Review of Symbolic Logic 4 (4):560-606.
To Distribute or Not to Distribute?Jean-Yves Béziau & Marcelo E. Coniglio - 2011 - Logic Journal of the IGPL 19 (4):466-583.
Decidability and Complexity of Fibred Logics Without Shared Connectives.Sérgio Marcelino & Carlos Caleiro - forthcoming - Logic Journal of the IGPL:jzw033.
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