In this talk I will discuss the main lines of research of universal logic and discuss its connection with the history and development of modern logic, that can be divided in three periods: the first dominated by questions related to the foundations of mathematics, the second when many different systems of logic were constructed in connection with artificial intelligence, linguistics, information theory, natural reasoning, etc., and the third period when people started to develop general frameworks and tools for the study of this huge variety of logic systems.

I will explain the basic ideas beyond universal logic. I will emphasize that it is a general theory of logics in the same way that universal algebra is a general theory of algebras and that universal logic is not a particular system of logic, applying to all situations. I will show that in fact it is impossible to develop such kind of universal system. I will argue that the relation between universal logic and the different logic systems can be understood in a way similar to what happens in linguistics. Linguistics is not a specific and universal language, but the study of how languages work and what a language is.

References
J.-Y.Béziau, «13 Questions about universal logic», Bulletin of the Section of Logic, 35 (2006), pp.133-150.
J.-Y.Béziau, «From consequence operator to universal logic: a survey of general abstract logic», in Logica Universalis, J.-Y.Béziau (ed), Birkhäuser, Basel , 2005, pp.3-17.
J.-Y.Béziau, « From paraconsistent to universal logic», Sorites, 12 (2001), pp.5-32.
J.-Y.Béziau, «Universal logic», in Logica’94 - Proceedings of the 8th International Symposium, T.Childers & O.Majer (eds), Prague, 1994, pp.73-93.