Combination of logics is still a fairly young subject. It arose from the study of some particular cases especially connected with modal logics, through the techniques of fusion, product and fibring. This was a first stage of the development of this new field of research, and afterwards the initial techniques (mainly fibring) were generalized to general logics. The techniques for combining logics help to the study of some fundamental phenomena of logic which are still not properly understood, connected to what a logic is and what are the relations between different formulations of a given logic. This tutorial, based on the book [2], is mainly devoted to the study of the so-called categorial fibring (or algebraic fibring), introduced in [1] and later on generalized to a wide class of logic systems such as modal (first-order) logics, higher-order logics and non-truth-functional logics, among others (see [2]).

The main topics to be analyzed herein are the following:

1. Fibring syntactically: The Hilbert calculi case

2. Fibring semantically: Interpretation systems and their fibring

3. Preservation results: Completenes and interpolation preservation by fibring

4. Heterogeneous fibring: Combining abstract proof systems

5. One step ahead: Fibring first-order (modal) logics

6. Still more generality: Fibring higher-order (modal) logics and non-truth-functional logics

7. The future: Graph-theoretic fibring

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

[2] W. Carnielli, M. Coniglio, D. Gabbay, P. Gouveia and C. Sernadas. Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems. Volume 35 of Applied Logic Series, Springer, 2008.

[3] A. Sernadas, C. Sernadas, J. Rasga and M. Coniglio. On Graph-theoretic Fibring of Logics. Journal of Logic and Computation, to appear.