Jean-Yves Beziau

Swiss National Science Foundation - Switzerland

The main philosophical ideas behind universal logic will be discussed: the analogy and difference with universal algebra, the key role of the notion of structure, the rejection of axioms and so on.
We will explain in particular what is the difference between this approach and the
traditional one.
We will describe various kinds of logical structures through a historical survey (Tarski's consequence operator, Hertz's Satzsysteme, etc).
Completeness will be given as an example of general theorem that can be re-presented  by cleary making the distinction between the particular and the universal.
We will present the main mathematical challenges raised by universal logic and  its philosophical import through some central problems such as combination of logics, translation and equivalence  between logics.
References
J.-Y.Beziau, "Universal Logic", in Logica'94,  T.Childers & O.Majer (eds), Czech
Academy of Sciences, Prague, 1994, pp.73-93.
J.-Y.Beziau, Researches on Universal Logic, PhD, University Denis Diderot,
Paris, 1995.
J.-Y.Beziau, "From paraconsistent logic to universal logic", Sorites, 12 (2001), pp.5-32.
J.-Y.Beziau (ed), Logica Universalis, Birkhaueser, Basel, 2005.