This tutorial is an introduction to the basic concepts of universal logic through  the study of classical  propositional logic (CPL), showing how  universal logic gives a new light to the most famous logical system of moden logic.

1. CPL as a Logical Structure

In this first session we will  explain what is the main idea of universal logic and how it makes sense to consider CPL from this point of view. We will examine the basic concepts of CPL,  propositions and connectives,  from this perspective explaining the philosophical mathematical values of this approach.  We will see how CPL can be deconstructed, reconstructed and defines in different ways. 

2. CPL in the Universe of Logics

In this second session we will study the place of CPL within the universe of logical structures, its relation with first-order classical logic and non-classical logics. This is a way to introduce two main topics of universal logic:  translations between logics and combinations of logics. 

3. CPL completeness theorem in a Universal Logic setting

 One aim of universal logic, following the spirit of modern mathematics, is to distinguish the general from the particular, in particular in the case of important theorems. We will study here as an example the case of the completeness theorem for CPL, examining what are the general features which can be extracted from it and apply to a  huge family of logical systems.

References

[1]  J.-Y.Beziau, “Classical negation can be expressed by one of its halves”, Logic Journal of the Interest Group in Pure and Applied Logics, 7 (1999), pp.145-151.

[2] J.-Y.Beziau, “The mathematical structure of logical syntax” in Advances in contemporary logic and computer science, W.A.Carnielli and I.M.L.D’Ottaviano (eds), American Mathematical Society, Providence, 1999, pp.1-17.

[3]  J.-Y.Beziau, “What is classical propositional logic?”, Logical Investigations, 8 (2001), pp.266-277. 

[5] J.-Y.Beziau, “Sequents and bivaluations”, Logique et Analyse, 44 (2001), pp.373-394.

[5] J.-Y.Beziau, “A paradox in the combination of logics’, in Workshop on Combination of Logics: Theory and Applications, W.A.Carnielli, F.M.Dionisio and P.Mateus (ed), IST, Lisbon, 2004, pp.75-78.