fibring

The logic produced by this operation, called constrained fibring, starts by considering two logics

Combining Logics Carnielli, Walter 2007

Algebraic fibring, to be described in Subsection is a good example of this approach.

Combining Logics Carnielli, Walter 2007

Profiting from universal constructions, in order to handle algebraic fibring, it is enough to define appropriate categories of signatures and logic systems.

Combining Logics Carnielli, Walter 2007

With respect to axiomatics, the logics obtained by fibring (or by a variant of fibring called dovetailing) can, in some cases, be axiomatized by the union of the (schema) axioms of the given logics.

Combining Logics Carnielli, Walter 2007

It should be noted that, by using a fixed set of schema variables for writing the axioms and rules of every calculus, the calculi obtained by fibring are also formed by schematic axioms and inference rules.

Combining Logics Carnielli, Walter 2007

However, if algebraic fibring is considered in categories such as those of Hilbert calculi or consequence relations, the combination between the logic of negation and the logic of disjunction results in a logic defined over ¬ and which is weaker than classical logic: the interaction law is no longer valid.

Combining Logics Carnielli, Walter 2007

This combination process, called unconstrained fibring, can be generalized, by allowing C1 and

Combining Logics Carnielli, Walter 2007

As it will be shown in Section the different notions of morphisms between logics affect the strength of the logics obtained by algebraic fibring in the different categories of logic systems.

Combining Logics Carnielli, Walter 2007

Moreover, the lack of a systematic definition of the axiomatization for the logics obtained by fibring is another negative aspect of this technique.

Combining Logics Carnielli, Walter 2007

Sernadas et al. 2002b, other examples of collapse were presented, and a solution to the problem was proposed by means of a controlled notion of algebraic fibring called modulated fibring.

Combining Logics Carnielli, Walter 2007