The first method of splicing logics, namely fibring, was introduced by Gabbay in 1996. That paper shows how two different systems can be unified in order to obtain a more complex system where specificities are mantained.

The fibring methodology explores the semantical aspect of the combination of two different logics, where the fibring function plays a fundamental role. Gabbay’s methodology, however, does not explain the syntactical aspect of the combination.

The categorial fibring introduced by A. Sernadas and his group gave a general process for combining logics by using the categorial language, and several question could be answered. Such approach makes clear that there are different ways to combine logics.

The cathodic systems are a taylor-suited, customized, class of paraconsistent modal systems obtained by a handmade procedure of combination. The completeness for this class reveals that the modal character is maintained in the combined system, and the only difference from the standard modal systems is the fact that the valuations inside worlds are paraconsistent, instead of classical.

In this talk I will compare different methods of combining logics in order to try to obtain the cathodic system CiS5 as a fribred product. Our hope is to find a method which could be able to capture the semantical character which was observed in the customized cathodic systems.

References

[Bueno-Soler, 2010] Bueno-Soler, J. (2010). Two Semantical Approaches to Paraconsistent Modalities. Logica Universalis (Print), v. 4, p. 137-160.

[Carnielli et al., 2008] Carnielli, W; Coniglio, M. E. ; Gabbay, D. ; Gouveia, P. ; Sernadas, C. Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems. Amsterdam: Springer, 2008

[Gabbay, 1999] Gabbay, D. (1999). Fibring Logics. Clarendon Press – Oxford.

[Sernadas et al., 1999] Sernadas, A., Sernadas, C. and Caleiro, C. (1999). Fibring of logics as a categorial construction. Journal of Logic and Computation, 9(2):149-179.