Topic: GENERAL LOGIC
The Meta-Fibring Environment: Preservation of meta-properties by fibring
By Marcelo E. Coniglio
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.