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ISSN 1519-9681
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ISSN 1519-9614
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Vol. 5(4), 2005 (Section Logic)
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The Meta-Fibring Environment:
Preservation of meta-properties by fibring
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Marcelo E. Coniglio
Personal web-page
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Date Posted: April, 26th 2005
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Revised Version - April 27th, 2007   [PDF]   [PS]
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.Abstract
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In this paper 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. This feature is obtained by changing the usual concept of morphism between logics (that is, a signature morphism preserving deductions) by a stronger one (a signature morphism preserving meta-implications between deductions). This allow us to obtain better results by fibring objects in Mcon and in Seq than using the usual notion of morphism between deduction systems: In fact, meta-fibring (that is, fibring in the proposed categories) avoids the phenomenon of fibring that we call anti-collapsing problem, as opposite to the well-known collapsing problem of fibring. Additionally, 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.
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