**Topic:**

**GENERAL LOGIC**

## The Meta-Fibring Environment: Preservation of meta-properties by fibring

By Marcelo E. Coniglio

In this paper the categoriesMconandSeqof 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 inMconand inSeqthan 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 inSeq(and, in particular, for objects inMcon) is proposed, obtaining a category of logic systems calledLog. A general theorem of preservation of completeness by fibring inLogis also obtained.

Source: CLE

Posted by Tony Marmo
at 21:42 BST

Updated: Tuesday, 26 April 2005 21:44 BST